diff --git a/changelog b/changelog index 693db6a..45e1388 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,15 @@ +20080112 tpd src/input/besselk.input complex gamma A&S reference regression +20080110 tpd src/input/Makefile add new regression test files +20080110 tpd src/input/asinhatanh.input create A&S reference regression +20080110 tpd src/input/sinhcosh.input create A&S reference regression +20080110 tpd src/input/tanhcoth.input create A&S reference regression +20080110 tpd src/input/asinatan.input create A&S reference regression +20080110 tpd src/input/seccsc.input create A&S reference regression +20080110 tpd src/input/tancot.input create A&S reference regression +20080109 tpd src/input/log.input create A&S reference regression +20080109 tpd src/input/sincos.input create A&S reference regression +20080108 tpd src/input/exp.input create A&S reference regression +20080108 tpd src/input/besselk.input update bibliography 20080107 tpd src/input/Makefile besselk.input regression test added 20080107 tpd src/input/besselk.input regression test added 20080107 tpd src/input/gamma.input missing file added diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index d727a41..07fca93 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -284,7 +284,8 @@ OUTS= ffrac.output \ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ allfact.regress antoine.regress \ arith.regress array1.regress array2.regress \ - arrows.regress assign.regress atansqrt.regress \ + arrows.regress asinatan.regress asinhatanh.regress \ + assign.regress atansqrt.regress \ asec.regress bags.regress bbtree.regress besselk.regress \ binary.regress bop.regress bstree.regress bouquet.regress \ bug100.regress bug101.regress \ @@ -306,6 +307,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ elt.regress eq.regress eqtbl.regress equation2.regress \ equation.regress evalex.regress eval.regress exdiff.regress \ exint.regress exit.regress exlap.regress exlimit.regress \ + exp.regress \ expexpan.regress explim.regress expr1.regress exprode.regress \ expr.regress exseries.regress exsum.regress exprpoly.regress \ farray.regress ffdemo.regress fferr.regress ffx72.regress \ @@ -329,6 +331,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ laplace.regress leg.regress limit.regress lindep.regress \ list.regress lode.regress lodesys.regress lodo1.regress \ lodo2.regress lodo3.regress lodof.regress lodo.regress \ + log.regress \ lpoly.regress lupfact.regress lword.regress macbug.regress \ macros.regress magma.regress mapleok.regress mappkg1.regress \ matbug.regress mathml.regress \ @@ -350,14 +353,16 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ realclos.regress reclos.regress repa6.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ schaum1.regress \ - scherk.regress scope.regress segbind.regress seg.regress \ + scherk.regress scope.regress seccsc.regress \ + segbind.regress seg.regress \ series2.regress series.regress sersolve.regress set.regress \ + sincos.regress sinhcosh.regress \ sincosex.regress sint.regress skew.regress slowint.regress \ solvetra.regress space3.regress sqmatrix.regress sregset.regress \ stbl.regress stream2.regress stream.regress streams.regress \ string.regress strtbl.regress summation.regress \ - symbol.regress t111293.regress \ - table.regress tanatan.regress textfile.regress torus.regress \ + symbol.regress t111293.regress table.regress tancot.regress \ + tanhcoth.regress tanatan.regress textfile.regress torus.regress \ triglim.regress tsetcatvermeer.regress tutchap1.regress \ void.regress uniseg.regress @@ -502,6 +507,7 @@ NAGLIB=${OUT}/c02aff.input ${OUT}/c02agf.input ${OUT}/c05adf.input \ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/alist.input ${OUT}/allfact.input ${OUT}/antoine.input \ ${OUT}/array1.input ${OUT}/array2.input ${OUT}/arrows.input \ + ${OUT}/asinatan.input ${OUT}/asinhatanh.input \ ${OUT}/assign.input ${OUT}/atansqrt.input ${OUT}/axiom.input \ ${OUT}/asec.input \ ${OUT}/bags.input ${OUT}/bbtree.input ${OUT}/besselk.input \ @@ -539,7 +545,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/elt.input \ ${OUT}/eq.input ${OUT}/eqtbl.input ${OUT}/equation.input \ ${OUT}/errortrap.input \ - ${OUT}/eval.input ${OUT}/exit.input ${OUT}/expexpan.input \ + ${OUT}/eval.input ${OUT}/exit.input ${OUT}/exp.input \ + ${OUT}/expexpan.input \ ${OUT}/explim.input ${OUT}/explot2d.input ${OUT}/explot3d.input \ ${OUT}/expr1.input ${OUT}/exprpoly.input \ ${OUT}/farray.input ${OUT}/ffdemo.input \ @@ -575,8 +582,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/lindep.input ${OUT}/liss1.input ${OUT}/liss2.input \ ${OUT}/list.input ${OUT}/lode.input ${OUT}/lodesys.input \ ${OUT}/lodo1.input ${OUT}/lodo2.input ${OUT}/lodof.input \ - ${OUT}/lodo.input ${OUT}/lodo3.input ${OUT}/lpoly.input \ - ${OUT}/lump.input \ + ${OUT}/lodo.input ${OUT}/lodo3.input ${OUT}/log.input \ + ${OUT}/lpoly.input ${OUT}/lump.input \ ${OUT}/lupfact.input ${OUT}/lword.input ${OUT}/macbug.input \ ${OUT}/macros.input ${OUT}/marcbench.input ${OUT}/magma.input \ ${OUT}/mapleok.input ${OUT}/mappkg1.input ${OUT}/matbug.input \ @@ -616,9 +623,10 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/schaum1.input \ ${OUT}/saddle.input \ - ${OUT}/scherk.input ${OUT}/scope.input \ + ${OUT}/scherk.input ${OUT}/scope.input ${OUT}/seccsc.input \ ${OUT}/segbind.input ${OUT}/seg.input ${OUT}/series2.input \ ${OUT}/series.input ${OUT}/sersolve.input ${OUT}/set.input \ + ${OUT}/sincos.input ${OUT}/sinhcosh.input \ ${OUT}/sincosex.input ${OUT}/sininv.input ${OUT}/sinsin.input \ ${OUT}/sinsin2.input ${OUT}/sint.input ${OUT}/skew.input \ ${OUT}/slowint.input ${OUT}/solvetra.input ${OUT}/space3.input \ @@ -628,7 +636,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/string.input ${OUT}/strtbl.input ${OUT}/summation.input \ ${OUT}/symbol.input \ ${OUT}/synonym.input ${OUT}/t111293.input \ - ${OUT}/table.input ${OUT}/tanatan.input ${OUT}/test.input \ + ${OUT}/table.input ${OUT}/tancot.input ${OUT}/tanhcoth.input \ + ${OUT}/tanatan.input ${OUT}/test.input \ ${OUT}/tetra.input ${OUT}/textfile.input ${OUT}/tknot.input \ ${OUT}/tree.input \ ${OUT}/triglim.input ${OUT}/tschirn.input ${OUT}/tsetcatbutcher.input \ @@ -684,7 +693,8 @@ DOCFILES= \ ${DOC}/as-eg3.input.dvi ${DOC}/as-eg4.input.dvi \ ${DOC}/as-eg5.input.dvi ${DOC}/aseg6.as.dvi \ ${DOC}/as-eg6.input.dvi ${DOC}/aseg7.as.dvi \ - ${DOC}/asec.input.dvi \ + ${DOC}/asec.input.dvi ${DOC}/asinatan.input.dvi \ + ${DOC}/asinhatanh.input.dvi \ ${DOC}/assign.input.dvi ${DOC}/atansqrt.input.dvi \ ${DOC}/axiom.input.dvi ${DOC}/bags.input.dvi \ ${DOC}/bbtree.input.dvi ${DOC}/besselk.input.dvi \ @@ -773,6 +783,7 @@ DOCFILES= \ ${DOC}/eval.input.dvi ${DOC}/exdiff.input.dvi \ ${DOC}/exint.input.dvi ${DOC}/exit.input.dvi \ ${DOC}/exlap.input.dvi ${DOC}/exlimit.input.dvi \ + ${DOC}/exp.input.dvi \ ${DOC}/expexpan.input.dvi ${DOC}/explim.input.dvi \ ${DOC}/explot2d.input.dvi ${DOC}/explot3d.input.dvi \ ${DOC}/expr1.input.dvi ${DOC}/expr.input.dvi \ @@ -854,6 +865,7 @@ DOCFILES= \ ${DOC}/lodesys.input.dvi ${DOC}/lodo1.input.dvi \ ${DOC}/lodo2.input.dvi ${DOC}/lodo3.input.dvi \ ${DOC}/lodof.input.dvi ${DOC}/lodo.input.dvi \ + ${DOC}/log.input.dvi \ ${DOC}/loop.input.dvi ${DOC}/lpoly.input.dvi \ ${DOC}/lump.input.dvi ${DOC}/lupfact.input.dvi \ ${DOC}/lword.input.dvi ${DOC}/macbug.input.dvi \ @@ -926,10 +938,12 @@ DOCFILES= \ ${DOC}/s21baf.input.dvi ${DOC}/s21bbf.input.dvi \ ${DOC}/s21bcf.input.dvi ${DOC}/s21bdf.input.dvi \ ${DOC}/saddle.input.dvi ${DOC}/scherk.input.dvi \ - ${DOC}/scope.input.dvi ${DOC}/segbind.input.dvi \ + ${DOC}/scope.input.dvi ${DOC}/seccsc.input.dvi \ + ${DOC}/segbind.input.dvi \ ${DOC}/seg.input.dvi ${DOC}/series2.input.dvi \ ${DOC}/series.input.dvi ${DOC}/sersolve.input.dvi \ - ${DOC}/set.input.dvi ${DOC}/sincosex.input.dvi \ + ${DOC}/set.input.dvi ${DOC}/sincos.input.dvi \ + ${DOC}/sinhcosh.input.dvi ${DOC}/sincosex.input.dvi \ ${DOC}/sininv.input.dvi ${DOC}/sinsin2.input.dvi \ ${DOC}/sinsin.input.dvi ${DOC}/sint.input.dvi \ ${DOC}/skew.input.dvi ${DOC}/slowint.input.dvi \ @@ -943,6 +957,7 @@ DOCFILES= \ ${DOC}/symbol.input.dvi ${DOC}/synonym2.input.dvi \ ${DOC}/synonym.input.dvi ${DOC}/t111293.input.dvi \ ${DOC}/table.input.dvi ${DOC}/tanatan.input.dvi \ + ${DOC}/tancot.input.dvi ${DOC}/tanhcoth.input.dvi \ ${DOC}/test.input.dvi ${DOC}/tetra.input.dvi \ ${DOC}/textfile.input.dvi ${DOC}/tknot.input.dvi \ ${DOC}/torus.input.dvi ${DOC}/tree.input.dvi \ diff --git a/src/input/asinatan.input.pamphlet b/src/input/asinatan.input.pamphlet new file mode 100644 index 0000000..a468c88 --- /dev/null +++ b/src/input/asinatan.input.pamphlet @@ -0,0 +1,456 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input asinatan.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This compares Axiom's asin and atan functions with the tables published in +Abramowitz and Stegun. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of asin(x), ranging from 0.01 to 1.00. The +second column is the reference value of tan from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp203-212 +<<*>>= +)spool asinatan.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.01,0.010000166674,asin(0.01),asin(0.01)-0.010000166674],_ +[0.02,0.020001333573,asin(0.02),asin(0.02)-0.020001333573],_ +[0.03,0.030004501823,asin(0.03),asin(0.03)-0.030004501823],_ +[0.04,0.040010674354,asin(0.04),asin(0.04)-0.040010674354],_ +[0.05,0.050020856806,asin(0.05),asin(0.05)-0.050020856806],_ +[0.06,0.060036058445,asin(0.06),asin(0.06)-0.060036058445],_ +[0.07,0.070057293088,asin(0.07),asin(0.07)-0.070057293088],_ +[0.08,0.080085580034,asin(0.08),asin(0.08)-0.080085580034],_ +[0.09,0.090121945015,asin(0.09),asin(0.09)-0.090121945015],_ +[0.10,0.100167421162,asin(0.10),asin(0.10)-0.100167421162],_ +[0.11,0.110223049988,asin(0.11),asin(0.11)-0.110223049988],_ +[0.12,0.120289882395,asin(0.12),asin(0.12)-0.120289882395],_ +[0.13,0.130368979703,asin(0.13),asin(0.13)-0.130368979703],_ +[0.14,0.140461414710,asin(0.14),asin(0.14)-0.140461414710],_ +[0.15,0.150568272777,asin(0.15),asin(0.15)-0.150568272777],_ +[0.16,0.160690652952,asin(0.16),asin(0.16)-0.160690652952],_ +[0.17,0.170829669129,asin(0.17),asin(0.17)-0.170829669129],_ +[0.18,0.180986451247,asin(0.18),asin(0.18)-0.180986451247],_ +[0.19,0.191162146531,asin(0.19),asin(0.19)-0.191162146531],_ +[0.20,0.201357920790,asin(0.20),asin(0.20)-0.201357920790],_ +[0.21,0.211574959758,asin(0.21),asin(0.21)-0.211574959758],_ +[0.22,0.221814470497,asin(0.22),asin(0.22)-0.221814470497],_ +[0.23,0.232077682863,asin(0.23),asin(0.23)-0.232077682863],_ +[0.24,0.242365851039,asin(0.24),asin(0.24)-0.242365851039],_ +[0.25,0.252680255142,asin(0.25),asin(0.25)-0.252680255142],_ +[0.26,0.263022202908,asin(0.26),asin(0.26)-0.263022202908],_ +[0.27,0.273393031467,asin(0.27),asin(0.27)-0.273393031467],_ +[0.28,0.283794109208,asin(0.28),asin(0.28)-0.283794109208],_ +[0.29,0.294226837749,asin(0.29),asin(0.29)-0.294226837749],_ +[0.30,0.304692654015,asin(0.30),asin(0.30)-0.304692654015],_ +[0.31,0.315193032441,asin(0.31),asin(0.31)-0.315193032441],_ +[0.32,0.325729487295,asin(0.32),asin(0.32)-0.325729487295],_ +[0.33,0.336303575154,asin(0.33),asin(0.33)-0.336303575154],_ +[0.34,0.346916897527,asin(0.34),asin(0.34)-0.346916897527],_ +[0.35,0.357571103646,asin(0.35),asin(0.35)-0.357571103646],_ +[0.36,0.368267893437,asin(0.36),asin(0.36)-0.368267893437],_ +[0.37,0.379009020696,asin(0.37),asin(0.37)-0.379009020696],_ +[0.38,0.389796296474,asin(0.38),asin(0.38)-0.389796296474],_ +[0.39,0.400631592701,asin(0.39),asin(0.39)-0.400631592701],_ +[0.40,0.411516846067,asin(0.40),asin(0.40)-0.411516846067],_ +[0.41,0.422454062187,asin(0.41),asin(0.41)-0.422454062187],_ +[0.42,0.433445320070,asin(0.42),asin(0.42)-0.433445320070],_ +[0.43,0.444492776936,asin(0.43),asin(0.43)-0.444492776936],_ +[0.44,0.455598673396,asin(0.44),asin(0.44)-0.455598673396],_ +[0.45,0.466765339047,asin(0.45),asin(0.45)-0.466765339047],_ +[0.46,0.477995198519,asin(0.46),asin(0.46)-0.477995198519],_ +[0.47,0.489290778014,asin(0.47),asin(0.47)-0.489290778014],_ +[0.48,0.500654712405,asin(0.48),asin(0.48)-0.500654712405],_ +[0.49,0.512089752934,asin(0.49),asin(0.49)-0.512089752934],_ +[0.50,0.523598775598,asin(0.50),asin(0.50)-0.523598775598],_ +[0.51,0.535184790276,asin(0.51),asin(0.51)-0.535184790276],_ +[0.52,0.546850950696,asin(0.52),asin(0.52)-0.546850950696],_ +[0.53,0.558600565343,asin(0.53),asin(0.53)-0.558600565343],_ +[0.54,0.570437109400,asin(0.54),asin(0.54)-0.570437109400],_ +[0.55,0.582364237869,asin(0.55),asin(0.55)-0.582364237869],_ +[0.56,0.594385800001,asin(0.56),asin(0.56)-0.594385800001],_ +[0.57,0.606505855213,asin(0.57),asin(0.57)-0.606505855213],_ +[0.58,0.618728690672,asin(0.58),asin(0.58)-0.618728690672],_ +[0.59,0.631058840778,asin(0.59),asin(0.59)-0.631058840778],_ +[0.60,0.643501108793,asin(0.60),asin(0.60)-0.643501108793],_ +[0.61,0.656060590925,asin(0.61),asin(0.61)-0.656060590925],_ +[0.62,0.668742703202,asin(0.62),asin(0.62)-0.668742703202],_ +[0.63,0.681553211563,asin(0.63),asin(0.63)-0.681553211563],_ +[0.64,0.694498265627,asin(0.64),asin(0.64)-0.694498265627],_ +[0.65,0.707584436725,asin(0.65),asin(0.65)-0.707584436725],_ +[0.66,0.720818760870,asin(0.66),asin(0.66)-0.720818760870],_ +[0.67,0.734208787453,asin(0.67),asin(0.67)-0.734208787453],_ +[0.68,0.747762634660,asin(0.68),asin(0.68)-0.747762634660],_ +[0.69,0.761489052748,asin(0.69),asin(0.69)-0.761489052748],_ +[0.70,0.775397496611,asin(0.70),asin(0.70)-0.775397496611],_ +[0.71,0.789498209346,asin(0.71),asin(0.71)-0.789498209346],_ +[0.72,0.803802318933,asin(0.72),asin(0.72)-0.803802318933],_ +[0.73,0.818321950632,asin(0.73),asin(0.73)-0.818321950632],_ +[0.74,0.833070358342,asin(0.74),asin(0.74)-0.833070358342],_ +[0.75,0.848062078981,asin(0.75),asin(0.75)-0.848062078981],_ +[0.76,0.863313115016,asin(0.76),asin(0.76)-0.863313115016],_ +[0.77,0.878841151669,asin(0.77),asin(0.77)-0.878841151669],_ +[0.78,0.894665817234,asin(0.78),asin(0.78)-0.894665817234],_ +[0.79,0.910808997407,asin(0.79),asin(0.79)-0.910808997407],_ +[0.80,0.927295218002,asin(0.80),asin(0.80)-0.927295218002],_ +[0.81,0.944152115154,asin(0.81),asin(0.81)-0.944152115154],_ +[0.82,0.961411018764,asin(0.82),asin(0.82)-0.961411018764],_ +[0.83,0.979107684368,asin(0.83),asin(0.83)-0.979107684368],_ +[0.84,0.997283222372,asin(0.84),asin(0.84)-0.997283222372],_ +[0.85,1.015985293815,asin(0.85),asin(0.85)-1.015985293815],_ +[0.86,1.035269672481,asin(0.86),asin(0.86)-1.035269672481],_ +[0.87,1.055202320549,asin(0.87),asin(0.87)-1.055202320549],_ +[0.88,1.075862200454,asin(0.88),asin(0.88)-1.075862200454],_ +[0.89,1.097345169523,asin(0.89),asin(0.89)-1.097345169523],_ +[0.90,1.119769514999,asin(0.90),asin(0.90)-1.119769514999],_ +[0.91,1.143284061850,asin(0.91),asin(0.91)-1.143284061850],_ +[0.92,1.168080485214,asin(0.92),asin(0.92)-1.168080485214],_ +[0.93,1.194412844477,asin(0.93),asin(0.93)-1.194412844477],_ +[0.94,1.222630305522,asin(0.94),asin(0.94)-1.222630305522],_ +[0.95,1.253235897503,asin(0.95),asin(0.95)-1.253235897503],_ +[0.96,1.287002217587,asin(0.96),asin(0.96)-1.287002217587],_ +[0.97,1.325230809280,asin(0.97),asin(0.97)-1.325230809280],_ +[0.98,1.370461484472,asin(0.98),asin(0.98)-1.370461484472],_ +[0.99,1.429256853470,asin(0.99),asin(0.99)-1.429256853470],_ +[1.00,1.570796326795,asin(1.00),asin(1.00)-1.570796326795]] +--R +--R +--R (1) +--R [[0.01,0.0100001666 74,0.0100001666 7416711312 6,0.167113126 E -12], +--R [0.02,0.0200013335 73,0.0200013335 7339049175 1,0.390491751 E -12], +--R [0.03,0.0300045018 23,0.0300045018 2347693769,0.47693769 E -12], +--R [0.04,0.0400106743 54,0.0400106743 5398892622 1,- 0.1107378 E -13], +--R [0.05,0.0500208568 06,0.0500208568 0577001466 3,- 0.229985337 E -12], +--R [0.06,0.0600360584 45,0.0600360584 452784225,0.2784225 E -12], +--R [0.07,0.0700572930 88,0.0700572930 8805025329 9,0.502533 E -13], +--R [0.08,0.0800855800 34,0.0800855800 3365901374 8,- 0.34098625 E -12], +--R [0.09,0.0901219450 15,0.0901219450 1459525581 5,- 0.40474419 E -12], +--R [0.1,0.1001674211 62,0.1001674211 6155979635,- 0.44020365 E -12], +--R [0.11,0.1102230499 88,0.1102230499 8774663318,- 0.25336682 E -12], +--R [0.12,0.1202898823 95,0.1202898823 9478807132,- 0.21192868 E -12], +--R [0.13,0.1303689797 03,0.1303689797 0314551294,0.14551294 E -12], +--R [0.14,0.1404614147 1,0.1404614147 0985580027,- 0.14419973 E -12], +--R [0.15,0.1505682727 77,0.1505682727 7668602642,- 0.31397358 E -12], +--R [0.16,0.1606906529 52,0.1606906529 5191060036,- 0.8939964 E -13], +--R [0.17,0.1708296691 29,0.1708296691 2910450072,0.1045007 E -12], +--R [0.18,0.1809864512 47,0.1809864512 4654770725,- 0.45229275 E -12], +--R [0.19,0.1911621465 31,0.1911621465 3105960346,0.5960346 E -13], +--R [0.2,0.2013579207 9,0.2013579207 9033079146,0.33079146 E -12], +--R [0.21,0.2115749597 58,0.2115749597 5809561381,0.9561381 E -13], +--R [0.22,0.2218144704 97,0.2218144704 9679441094,- 0.20558906 E -12], +--R [0.23,0.2320776828 63,0.2320776828 6271317742,- 0.28682258 E -12], +--R [0.24,0.2423658510 39,0.2423658510 3896323277,- 0.3676723 E -13], +--R [0.25,0.2526802551 42,0.2526802551 4207865349,0.7865349 E -13], +--R [0.26,0.2630222029 08,0.2630222029 0846889582,0.46889582 E -12], +--R [0.27,0.2733930314 67,0.2733930314 6747322258,0.47322258 E -12], +--R [0.28,0.2837941092 08,0.2837941092 0832784562,0.32784563 E -12], +--R [0.29,0.2942268377 49,0.2942268377 4898247936,- 0.175206 E -13], +--R [0.3,0.3046926540 15,0.3046926540 1539750797,0.39750797 E -12], +--R [0.31,0.3151930324 41,0.3151930324 4072444134,- 0.27555866 E -12], +--R [0.32,0.3257294872 95,0.3257294872 9463015931,- 0.36984069 E -12], +--R [0.33,0.3363035751 54,0.3363035751 5398034192,- 0.196581 E -13], +--R [0.34,0.3469168975 27,0.3469168975 2716170922,0.1617092 E -12], +--R [0.35,0.3575711036 46,0.3575711036 4551028671,- 0.48971329 E -12], +--R [0.36,0.3682678934 37,0.3682678934 3663998093,- 0.36001907 E -12], +--R [0.37,0.3790090206 96,0.3790090206 9595081407,- 0.4918592 E -13], +--R [0.38,0.3897962964 74,0.3897962964 7426056359,0.26056359 E -12], +--R [0.39,0.4006315927 01,0.4006315927 0137191121,0.37191121 E -12], +--R [0.4,0.4115168460 67,0.4115168460 6748801938,0.48801938 E -12], +--R [0.41,0.4224540621 87,0.4224540621 8675575657,- 0.24424343 E -12], +--R [0.42,0.4334453200 7,0.4334453200 6988597641,- 0.1140236 E -12], +--R [0.43,0.4444927769 36,0.4444927769 3581903875,- 0.1809612 E -12], +--R [0.44,0.4555986733 96,0.4555986733 9582336298,- 0.176637 E -12], +--R [0.45,0.4667653390 47,0.4667653390 4729636185,0.29636185 E -12], +--R [0.46,0.4779951985 19,0.4779951985 1895237921,- 0.4762079 E -13], +--R [0.47,0.4892907780 14,0.4892907780 1411571422,0.1157142 E -12], +--R [0.48,0.5006547124 05,0.5006547124 0458816211,- 0.4118379 E -12], +--R [0.49,0.5120897529 34,0.5120897529 3414777137,0.1477714 E -12], +--R [0.5,0.5235987755 98,0.5235987755 9829887308,0.2988731 E -12], +--R [0.51,0.5351847902 76,0.5351847902 7559984754,- 0.4001525 E -12], +--R [0.52,0.5468509506 96,0.5468509506 9594410879,- 0.558912 E -13], +--R [0.53,0.5586005653 43,0.5586005653 4280071945,- 0.1992805 E -12], +--R [0.54,0.5704371094,0.5704371093 9992190735,- 0.7809265 E -13], +--R [0.55,0.5823642378 69,0.5823642378 6874344183,- 0.2565582 E -12], +--R [0.56,0.5943858000 01,0.5943858000 0106220388,0.6220388 E -13], +--R [0.57,0.6065058552 13,0.6065058552 1308694718,0.8694718 E -13], +--R [0.58,0.6187286906 72,0.6187286906 7225109051,0.2510905 E -12], +--R [0.59,0.6310588407 78,0.6310588407 7802138008,0.213801 E -13], +--R [0.6,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12], +--R [0.61,0.6560605909 25,0.6560605909 2492264451,- 0.7735549 E -13], +--R [0.62,0.6687427032 02,0.6687427032 0237175414,0.3717541 E -12], +--R [0.63,0.6815532115 63,0.6815532115 6311692392,0.1169239 E -12], +--R [0.64,0.6944982656 27,0.6944982656 2655598784,- 0.4440122 E -12], +--R [0.65,0.7075844367 25,0.7075844367 2535557545,0.3555755 E -12], +--R [0.66,0.7208187608 7,0.7208187608 7008963003,0.8963003 E -13], +--R [0.67,0.7342087874 53,0.7342087874 533589103,0.3589103 E -12], +--R [0.68,0.7477626346 6,0.7477626346 5992058046,- 0.7941954 E -13], +--R [0.69,0.7614890527 48,0.7614890527 4763322831,- 0.3667717 E -12], +--R [0.7,0.7753974966 11,0.7753974966 1075306374,- 0.2469363 E -12], +--R [0.71,0.7894982093 46,0.7894982093 4617197301,0.171973 E -12], +--R [0.72,0.8038023189 33,0.8038023189 3303003221,0.300322 E -13], +--R [0.73,0.8183219506 32,0.8183219506 3155981721,- 0.4401828 E -12], +--R [0.74,0.8330703583 42,0.8330703583 4164781149,- 0.3521885 E -12], +--R [0.75,0.8480620789 81,0.8480620789 8148100805,0.48100805 E -12], +--R [0.76,0.8633131150 16,0.8633131150 1555364761,- 0.4463524 E -12], +--R [0.77,0.8788411516 69,0.8788411516 6857970602,- 0.420294 E -12], +--R [0.78,0.8946658172 34,0.8946658172 3423520948,0.2352095 E -12], +--R [0.79,0.9108089974 07,0.9108089974 0739818925,0.3981893 E -12], +--R [0.8,0.9272952180 02,0.9272952180 0161223243,- 0.3877676 E -12], +--R [0.81,0.9441521151 54,0.9441521151 5415595048,0.1559505 E -12], +--R [0.82,0.9614110187 64,0.9614110187 6410160329,0.1016033 E -12], +--R [0.83,0.9791076843 68,0.9791076843 6835265479,0.3526548 E -12], +--R [0.84,0.9972832223 72,0.9972832223 7179986605,- 0.2001339 E -12], +--R [0.85,1.0159852938 15,1.0159852938 148251312,- 0.1748688 E -12], +--R [0.86,1.0352696724 81,1.0352696724 805087973,- 0.4912027 E -12], +--R [0.87,1.0552023205 49,1.0552023205 488061213,- 0.1938787 E -12], +--R [0.88,1.0758622004 54,1.0758622004 540010964,0.10964 E -14], +--R [0.89,1.0973451695 23,1.0973451695 228303977,- 0.1696023 E -12], +--R [0.9,1.1197695149 99,1.1197695149 986341867,- 0.3658133 E -12], +--R [0.91,1.1432840618 5,1.1432840618 500270323,0.270323 E -13], +--R [0.92,1.1680804852 14,1.1680804852 142350363,0.2350363 E -12], +--R [0.93,1.1944128444 77,1.1944128444 771683741,0.1683741 E -12], +--R [0.94,1.2226303055 22,1.2226303055 21935738,- 0.64262 E -13], +--R [0.95,1.2532358975 03,1.2532358975 033752587,0.3752587 E -12], +--R [0.96,1.2870022175 87,1.2870022175 865687736,- 0.4312264 E -12], +--R [0.97,1.3252308092 8,1.3252308092 796046112,- 0.3953888 E -12], +--R [0.98,1.3704614844 72,1.3704614844 717770265,- 0.2229735 E -12], +--R [0.99,1.4292568534 7,1.4292568534 704694005,0.4694005 E -12], +--R [1.0,1.5707963267 95,1.5707963267 948966192,- 0.103381 E -12]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of atan(x), ranging from 0.01 to 1.00. The +second column is the reference value of tan from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp203-212 +<<*>>= + +--S 2 of 2 +[[0.01,0.009999666687,atan(0.01),atan(0.01)-0.009999666687],_ +[0.02,0.019997333973,atan(0.02),atan(0.02)-0.019997333973],_ +[0.03,0.029991004857,atan(0.03),atan(0.03)-0.029991004857],_ +[0.04,0.039978687123,atan(0.04),atan(0.04)-0.039978687123],_ +[0.05,0.049958395722,atan(0.05),atan(0.05)-0.049958395722],_ +[0.06,0.059928155121,atan(0.06),atan(0.06)-0.059928155121],_ +[0.07,0.069886001635,atan(0.07),atan(0.07)-0.069886001635],_ +[0.08,0.079829985712,atan(0.08),atan(0.08)-0.079829985712],_ +[0.09,0.089758174190,atan(0.09),atan(0.09)-0.089758174190],_ +[0.10,0.099668652491,atan(0.10),atan(0.10)-0.099668652491],_ +[0.11,0.109559526774,atan(0.11),atan(0.11)-0.109559526774],_ +[0.12,0.119428926018,atan(0.12),atan(0.12)-0.119428926018],_ +[0.13,0.129275004048,atan(0.13),atan(0.13)-0.129275004048],_ +[0.14,0.139095941482,atan(0.14),atan(0.14)-0.139095941482],_ +[0.15,0.148889947609,atan(0.15),atan(0.15)-0.148889947609],_ +[0.16,0.158655262186,atan(0.16),atan(0.16)-0.158655262186],_ +[0.17,0.168390157148,atan(0.17),atan(0.17)-0.168390157148],_ +[0.18,0.178092938231,atan(0.18),atan(0.18)-0.178092938231],_ +[0.19,0.187761946514,atan(0.19),atan(0.19)-0.187761946514],_ +[0.20,0.197395559850,atan(0.20),atan(0.20)-0.197395559850],_ +[0.21,0.206992194220,atan(0.21),atan(0.21)-0.206992194220],_ +[0.22,0.216550304976,atan(0.22),atan(0.22)-0.216550304976],_ +[0.23,0.226068387994,atan(0.23),atan(0.23)-0.226068387994],_ +[0.24,0.235544980721,atan(0.24),atan(0.24)-0.235544980721],_ +[0.25,0.244978663127,atan(0.25),atan(0.25)-0.244978663127],_ +[0.26,0.254368058553,atan(0.26),atan(0.26)-0.254368058553],_ +[0.27,0.263711834462,atan(0.27),atan(0.27)-0.263711834462],_ +[0.28,0.273008703087,atan(0.28),atan(0.28)-0.273008703087],_ +[0.29,0.282257421981,atan(0.29),atan(0.29)-0.282257421981],_ +[0.30,0.291456794478,atan(0.30),atan(0.30)-0.291456794478],_ +[0.31,0.300605670042,atan(0.31),atan(0.31)-0.300605670042],_ +[0.32,0.309702944542,atan(0.32),atan(0.32)-0.309702944542],_ +[0.33,0.318747560421,atan(0.33),atan(0.33)-0.318747560421],_ +[0.34,0.327738506781,atan(0.34),atan(0.34)-0.327738506781],_ +[0.35,0.336674819387,atan(0.35),atan(0.35)-0.336674819387],_ +[0.36,0.345555580582,atan(0.36),atan(0.36)-0.345555580582],_ +[0.37,0.354379919123,atan(0.37),atan(0.37)-0.354379919123],_ +[0.38,0.363147009946,atan(0.38),atan(0.38)-0.363147009946],_ +[0.39,0.371856073849,atan(0.39),atan(0.39)-0.371856073849],_ +[0.40,0.380506377112,atan(0.40),atan(0.40)-0.380506377112],_ +[0.41,0.389097231055,atan(0.41),atan(0.41)-0.389097231055],_ +[0.42,0.397627991522,atan(0.42),atan(0.42)-0.397627991522],_ +[0.43,0.406098058318,atan(0.43),atan(0.43)-0.406098058318],_ +[0.44,0.414506874585,atan(0.44),atan(0.44)-0.414506874585],_ +[0.45,0.422853926133,atan(0.45),atan(0.45)-0.422853926133],_ +[0.46,0.431138740719,atan(0.46),atan(0.46)-0.431138740719],_ +[0.47,0.439360887285,atan(0.47),atan(0.47)-0.439360887285],_ +[0.48,0.447519975157,atan(0.48),atan(0.48)-0.447519975157],_ +[0.49,0.455615653211,atan(0.49),atan(0.49)-0.455615653211],_ +[0.50,0.463647609001,atan(0.50),atan(0.50)-0.463647609001],_ +[0.51,0.471615567862,atan(0.51),atan(0.51)-0.471615567862],_ +[0.52,0.479519291993,atan(0.52),atan(0.52)-0.479519291993],_ +[0.53,0.487358579505,atan(0.53),atan(0.53)-0.487358579505],_ +[0.54,0.495133263468,atan(0.54),atan(0.54)-0.495133263468],_ +[0.55,0.502843210928,atan(0.55),atan(0.55)-0.502843210928],_ +[0.56,0.510488321917,atan(0.56),atan(0.56)-0.510488321917],_ +[0.57,0.518068528457,atan(0.57),atan(0.57)-0.518068528457],_ +[0.58,0.525583793552,atan(0.58),atan(0.58)-0.525583793552],_ +[0.59,0.533034110177,atan(0.59),atan(0.59)-0.533034110177],_ +[0.60,0.540419500271,atan(0.60),atan(0.60)-0.540419500271],_ +[0.61,0.547740013716,atan(0.61),atan(0.61)-0.547740013716],_ +[0.62,0.554995727339,atan(0.62),atan(0.62)-0.554995727339],_ +[0.63,0.562186743900,atan(0.63),atan(0.63)-0.562186743900],_ +[0.64,0.569313191101,atan(0.64),atan(0.64)-0.569313191101],_ +[0.65,0.576375220591,atan(0.65),atan(0.65)-0.576375220591],_ +[0.66,0.583373006994,atan(0.66),atan(0.66)-0.583373006994],_ +[0.67,0.590306746935,atan(0.67),atan(0.67)-0.590306746935],_ +[0.68,0.597176658093,atan(0.68),atan(0.68)-0.597176658093],_ +[0.69,0.603982978253,atan(0.69),atan(0.69)-0.603982978253],_ +[0.70,0.610725964389,atan(0.70),atan(0.70)-0.610725964389],_ +[0.71,0.617405891752,atan(0.71),atan(0.71)-0.617405891752],_ +[0.72,0.624023052977,atan(0.72),atan(0.72)-0.624023052977],_ +[0.73,0.630577757215,atan(0.73),atan(0.73)-0.630577757215],_ +[0.74,0.637070329276,atan(0.74),atan(0.74)-0.637070329276],_ +[0.75,0.643501108793,atan(0.75),atan(0.75)-0.643501108793],_ +[0.76,0.649870449412,atan(0.76),atan(0.76)-0.649870449412],_ +[0.77,0.656178717991,atan(0.77),atan(0.77)-0.656178717991],_ +[0.78,0.662426293833,atan(0.78),atan(0.78)-0.662426293833],_ +[0.79,0.668613567928,atan(0.79),atan(0.79)-0.668613567928],_ +[0.80,0.674740942224,atan(0.80),atan(0.80)-0.674740942224],_ +[0.81,0.680808828916,atan(0.81),atan(0.81)-0.680808828916],_ +[0.82,0.686817649759,atan(0.82),atan(0.82)-0.686817649759],_ +[0.83,0.692767835397,atan(0.83),atan(0.83)-0.692767835397],_ +[0.84,0.698659824721,atan(0.84),atan(0.84)-0.698659824721],_ +[0.85,0.704494064242,atan(0.85),atan(0.85)-0.704494064242],_ +[0.86,0.710271007487,atan(0.86),atan(0.86)-0.710271007487],_ +[0.87,0.715991114416,atan(0.87),atan(0.87)-0.715991114416],_ +[0.88,0.721654850865,atan(0.88),atan(0.88)-0.721654850865],_ +[0.89,0.727262687997,atan(0.89),atan(0.89)-0.727262687997],_ +[0.90,0.732815101787,atan(0.90),atan(0.90)-0.732815101787],_ +[0.91,0.738312572517,atan(0.91),atan(0.91)-0.738312572517],_ +[0.92,0.743755584299,atan(0.92),atan(0.92)-0.743755584299],_ +[0.93,0.749144624606,atan(0.93),atan(0.93)-0.749144624606],_ +[0.94,0.754480183834,atan(0.94),atan(0.94)-0.754480183834],_ +[0.95,0.759762754876,atan(0.95),atan(0.95)-0.759762754876],_ +[0.96,0.764992832711,atan(0.96),atan(0.96)-0.764992832711],_ +[0.97,0.770170914020,atan(0.97),atan(0.97)-0.770170914020],_ +[0.98,0.775297496812,atan(0.98),atan(0.98)-0.775297496812],_ +[0.99,0.780373080067,atan(0.99),atan(0.99)-0.780373080067],_ +[1.00,0.785398163397,atan(1.00),atan(1.00)-0.785398163397]] +--R +--R +--R (2) +--R [[0.01,0.0099996666 87,0.0099996666 8666523820 63,- 0.334761794 E -12], +--R [0.02,0.0199973339 73,0.0199973339 7315053306 1,0.150533061 E -12], +--R [0.03,0.0299910048 57,0.0299910048 5687789967 7,- 0.122100323 E -12], +--R [0.04,0.0399786871 23,0.0399786871 2329004141 4,0.290041414 E -12], +--R [0.05,0.0499583957 22,0.0499583957 2194276141,- 0.5723859 E -13], +--R [0.06,0.0599281551 21,0.0599281551 2120788443 2,0.20788443 E -12], +--R [0.07,0.0698860016 35,0.0698860016 3464249929 5,- 0.35750071 E -12], +--R [0.08,0.0798299857 12,0.0798299857 1223731589 3,0.23731589 E -12], +--R [0.09,0.0897581741 9,0.0897581741 8995052315,- 0.4947685 E -13], +--R [0.1,0.0996686524 91,0.0996686524 9116202737 9,0.16202738 E -12], +--R [0.11,0.1095595267 74,0.1095595267 7394434487,- 0.5565513 E -13], +--R [0.12,0.1194289260 18,0.1194289260 1833845181,0.33845181 E -12], +--R [0.13,0.1292750040 48,0.1292750040 4814305472,0.14305472 E -12], +--R [0.14,0.1390959414 82,0.1390959414 820713243,0.713243 E -13], +--R [0.15,0.1488899476 09,0.1488899476 0949725059,0.49725059 E -12], +--R [0.16,0.1586552621 86,0.1586552621 8640140386,0.40140386 E -12], +--R [0.17,0.1683901571 48,0.1683901571 4752989727,- 0.47010272 E -12], +--R [0.18,0.1780929382 31,0.1780929382 3119754967,0.19754967 E -12], +--R [0.19,0.1877619465 14,0.1877619465 135934152,- 0.4065848 E -12], +--R [0.2,0.1973955598 5,0.1973955598 4988075837,- 0.11924163 E -12], +--R [0.21,0.2069921942 2,0.2069921942 198210249,- 0.1789751 E -12], +--R [0.22,0.2165503049 76,0.2165503049 7608927648,0.8927648 E -13], +--R [0.23,0.2260683879 94,0.2260683879 9388390584,- 0.11609416 E -12], +--R [0.24,0.2355449807 21,0.2355449807 2086334143,- 0.13665857 E -12], +--R [0.25,0.2449786631 27,0.2449786631 2686415417,- 0.13584583 E -12], +--R [0.26,0.2543680585 53,0.2543680585 5326593143,0.26593143 E -12], +--R [0.27,0.2637118344 62,0.2637118344 6226612016,0.26612016 E -12], +--R [0.28,0.2730087030 87,0.2730087030 8671060295,- 0.28939705 E -12], +--R [0.29,0.2822574219 81,0.2822574219 8149112127,0.49112127 E -12], +--R [0.3,0.2914567944 78,0.2914567944 77867092,- 0.132908 E -12], +--R [0.31,0.3006056700 42,0.3006056700 4239540423,0.39540423 E -12], +--R [0.32,0.3097029445 42,0.3097029445 4245619992,0.45619992 E -12], +--R [0.33,0.3187475604 21,0.3187475604 2064443712,- 0.35556288 E -12], +--R [0.34,0.3277385067 81,0.3277385067 80555446,- 0.444554 E -12], +--R [0.35,0.3366748193 87,0.3366748193 867271814,- 0.2728186 E -12], +--R [0.36,0.3455555805 82,0.3455555805 8171213686,- 0.28786314 E -12], +--R [0.37,0.3543799191 23,0.3543799191 2343780983,0.43780983 E -12], +--R [0.38,0.3631470099 46,0.3631470099 4617628972,0.1762897 E -12], +--R [0.39,0.3718560738 49,0.3718560738 485812575,- 0.4187425 E -12], +--R [0.4,0.3805063771 12,0.3805063771 123648863,0.3648863 E -12], +--R [0.41,0.3890972310 55,0.3890972310 5527841924,0.27841924 E -12], +--R [0.42,0.3976279915 22,0.3976279915 22129314,0.129314 E -12], +--R [0.43,0.4060980583 18,0.4060980583 1761564783,- 0.38435217 E -12], +--R [0.44,0.4145068745 85,0.4145068745 8478593834,- 0.2140617 E -12], +--R [0.45,0.4228539261 33,0.4228539261 3294071297,- 0.5928703 E -13], +--R [0.46,0.4311387407 19,0.4311387407 1878218339,- 0.2178166 E -12], +--R [0.47,0.4393608872 85,0.4393608872 8459143742,- 0.40856258 E -12], +--R [0.48,0.4475199751 57,0.4475199751 5716987972,0.1698797 E -12], +--R [0.49,0.4556156532 11,0.4556156532 1122449214,0.2244921 E -12], +--R [0.5,0.4636476090 01,0.4636476090 0080611621,- 0.1938838 E -12], +--R [0.51,0.4716155678 62,0.4716155678 6232766012,0.32766012 E -12], +--R [0.52,0.4795192919 93,0.4795192919 9259616542,- 0.40383458 E -12], +--R [0.53,0.4873585795 05,0.4873585795 0519028312,0.1902831 E -12], +--R [0.54,0.4951332634 68,0.4951332634 6840412185,0.40412185 E -12], +--R [0.55,0.5028432109 28,0.5028432109 2786082733,- 0.1391727 E -12], +--R [0.56,0.5104883219 17,0.5104883219 1677576997,- 0.22423 E -12], +--R [0.57,0.5180685284 57,0.5180685284 56720949,- 0.279051 E -12], +--R [0.58,0.5255837935 52,0.5255837935 5161020277,- 0.3897972 E -12], +--R [0.59,0.5330341101 77,0.5330341101 7749002604,0.49002604 E -12], +--R [0.6,0.5404195002 71,0.5404195002 7058415544,- 0.4158446 E -12], +--R [0.61,0.5477400137 16,0.5477400137 1590245052,- 0.9754948 E -13], +--R [0.62,0.5549957273 39,0.5549957273 3858676242,- 0.4132376 E -12], +--R [0.63,0.5621867439,0.5621867439 0002917485,0.291748 E -13], +--R [0.64,0.5693131911 01,0.5693131911 0066188631,- 0.3381137 E -12], +--R [0.65,0.5763752205 91,0.5763752205 9118368022,0.1836802 E -12], +--R [0.66,0.5833730069 94,0.5833730069 9385593947,- 0.1440605 E -12], +--R [0.67,0.5903067469 35,0.5903067469 3537198239,0.3719824 E -12], +--R [0.68,0.5971766580 93,0.5971766580 9267754844,- 0.3224516 E -12], +--R [0.69,0.6039829782 53,0.6039829782 5299790738,- 0.20926 E -14], +--R [0.7,0.6107259643 89,0.6107259643 8920861654,0.2086165 E -12], +--R [0.71,0.6174058917 52,0.6174058917 5157266652,- 0.4273335 E -12], +--R [0.72,0.6240230529 77,0.6240230529 7675684759,- 0.2431524 E -12], +--R [0.73,0.6305777572 15,0.6305777572 1493480666,- 0.6519333 E -13], +--R [0.74,0.6370703292 76,0.6370703292 7568357172,- 0.3164283 E -12], +--R [0.75,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12], +--R [0.76,0.6498704494 12,0.6498704494 1194757749,- 0.524225 E -13], +--R [0.77,0.6561787179 91,0.6561787179 9139487538,0.3948754 E -12], +--R [0.78,0.6624262938 33,0.6624262938 3315116177,0.1511618 E -12], +--R [0.79,0.6686135679 28,0.6686135679 2782091069,- 0.1790893 E -12], +--R [0.8,0.6747409422 24,0.6747409422 2355266306,- 0.4473369 E -12], +--R [0.81,0.6808088289 16,0.6808088289 1582756649,- 0.1724335 E -12], +--R [0.82,0.6868176497 59,0.6868176497 5864527553,- 0.3547245 E -12], +--R [0.83,0.6927678353 97,0.6927678353 9712221066,0.1222107 E -12], +--R [0.84,0.6986598247 21,0.6986598247 214631978,0.4631978 E -12], +--R [0.85,0.7044940642 42,0.7044940642 4221771666,0.2177167 E -12], +--R [0.86,0.7102710074 87,0.7102710074 8668623033,- 0.3137697 E -12], +--R [0.87,0.7159911144 16,0.7159911144 1630019894,0.3001989 E -12], +--R [0.88,0.7216548508 65,0.7216548508 6476123707,- 0.2387629 E -12], +--R [0.89,0.7272626879 97,0.7272626879 9669029805,- 0.309702 E -12], +--R [0.9,0.7328151017 87,0.7328151017 8650659164,- 0.49340836 E -12], +--R [0.91,0.7383125725 17,0.7383125725 1722800021,0.2280002 E -12], +--R [0.92,0.7437555842 99,0.7437555842 9885988576,- 0.1401142 E -12], +--R [0.93,0.7491446246 06,0.7491446246 0601721032,0.172103 E -13], +--R [0.94,0.7544801838 34,0.7544801838 3440566231,0.4056623 E -12], +--R [0.95,0.7597627548 76,0.7597627548 7577082892,- 0.2291711 E -12], +--R [0.96,0.7649928327 11,0.7649928327 1091022317,- 0.8977683 E -13], +--R [0.97,0.7701709140 2,0.7701709140 2033100726,0.3310073 E -12], +--R [0.98,0.7752974968 12,0.7752974968 1212640304,0.126403 E -12], +--R [0.99,0.7803730800 67,0.7803730800 666358989,- 0.3641011 E -12], +--R [1.0,0.7853981633 97,0.7853981633 9744830961,0.4483096 E -12]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp203-212 +\end{thebibliography} +\end{document} + diff --git a/src/input/asinhatanh.input.pamphlet b/src/input/asinhatanh.input.pamphlet new file mode 100644 index 0000000..b0c7783 --- /dev/null +++ b/src/input/asinhatanh.input.pamphlet @@ -0,0 +1,460 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input asinhatanh.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is a set of tests for the tanh and coth functions. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of asinh, ranging from 0.00 to 1.00. The +second column is the reference value of asinh from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp221 + +<<*>>= +)spool asinhatanh.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.00,0.000000000,asinh(0.00),asinh(0.00)-0.000000000],_ +[0.01,0.009999833,asinh(0.01),asinh(0.01)-0.009999833],_ +[0.02,0.019998667,asinh(0.02),asinh(0.02)-0.019998667],_ +[0.03,0.029995502,asinh(0.03),asinh(0.03)-0.029995502],_ +[0.04,0.039989341,asinh(0.04),asinh(0.04)-0.039989341],_ +[0.05,0.049979190,asinh(0.05),asinh(0.05)-0.049979190],_ +[0.06,0.059964058,asinh(0.06),asinh(0.06)-0.059964058],_ +[0.07,0.069942959,asinh(0.07),asinh(0.07)-0.069942959],_ +[0.08,0.079914912,asinh(0.08),asinh(0.08)-0.079914912],_ +[0.09,0.089878941,asinh(0.09),asinh(0.09)-0.089878941],_ +[0.10,0.099834079,asinh(0.10),asinh(0.10)-0.099834079],_ +[0.11,0.109779366,asinh(0.11),asinh(0.11)-0.109779366],_ +[0.12,0.119713851,asinh(0.12),asinh(0.12)-0.119713851],_ +[0.13,0.129636590,asinh(0.13),asinh(0.13)-0.129636590],_ +[0.14,0.139546654,asinh(0.14),asinh(0.14)-0.139546654],_ +[0.15,0.149443120,asinh(0.15),asinh(0.15)-0.149443120],_ +[0.16,0.159325080,asinh(0.16),asinh(0.16)-0.159325080],_ +[0.17,0.169191636,asinh(0.17),asinh(0.17)-0.169191636],_ +[0.18,0.179041904,asinh(0.18),asinh(0.18)-0.179041904],_ +[0.19,0.188875015,asinh(0.19),asinh(0.19)-0.188875015],_ +[0.20,0.198690110,asinh(0.20),asinh(0.20)-0.198690110],_ +[0.21,0.208486350,asinh(0.21),asinh(0.21)-0.208486350],_ +[0.22,0.218262908,asinh(0.22),asinh(0.22)-0.218262908],_ +[0.23,0.228018972,asinh(0.23),asinh(0.23)-0.228018972],_ +[0.24,0.237753749,asinh(0.24),asinh(0.24)-0.237753749],_ +[0.25,0.247466462,asinh(0.25),asinh(0.25)-0.247466462],_ +[0.26,0.257156349,asinh(0.26),asinh(0.26)-0.257156349],_ +[0.27,0.266822667,asinh(0.27),asinh(0.27)-0.266822667],_ +[0.28,0.276464691,asinh(0.28),asinh(0.28)-0.276464691],_ +[0.29,0.286081715,asinh(0.29),asinh(0.29)-0.286081715],_ +[0.30,0.295673048,asinh(0.30),asinh(0.30)-0.295673048],_ +[0.31,0.305238020,asinh(0.31),asinh(0.31)-0.305238020],_ +[0.32,0.314775980,asinh(0.32),asinh(0.32)-0.314775980],_ +[0.33,0.324286295,asinh(0.33),asinh(0.33)-0.324286295],_ +[0.34,0.333768352,asinh(0.34),asinh(0.34)-0.333768352],_ +[0.35,0.343221555,asinh(0.35),asinh(0.35)-0.343221555],_ +[0.36,0.352645330,asinh(0.36),asinh(0.36)-0.352645330],_ +[0.37,0.362039121,asinh(0.37),asinh(0.37)-0.362039121],_ +[0.38,0.371402391,asinh(0.38),asinh(0.38)-0.371402391],_ +[0.39,0.380734624,asinh(0.39),asinh(0.39)-0.380734624],_ +[0.40,0.390035320,asinh(0.40),asinh(0.40)-0.390035320],_ +[0.41,0.399304001,asinh(0.41),asinh(0.41)-0.399304001],_ +[0.42,0.408540208,asinh(0.42),asinh(0.42)-0.408540208],_ +[0.43,0.417743500,asinh(0.43),asinh(0.43)-0.417743500],_ +[0.44,0.426913454,asinh(0.44),asinh(0.44)-0.426913454],_ +[0.45,0.436049669,asinh(0.45),asinh(0.45)-0.436049669],_ +[0.46,0.445151759,asinh(0.46),asinh(0.46)-0.445151759],_ +[0.47,0.454219359,asinh(0.47),asinh(0.47)-0.454219359],_ +[0.48,0.463252120,asinh(0.48),asinh(0.48)-0.463252120],_ +[0.49,0.472249713,asinh(0.49),asinh(0.49)-0.472249713],_ +[0.50,0.481211825,asinh(0.50),asinh(0.50)-0.481211825],_ +[0.51,0.490138161,asinh(0.51),asinh(0.51)-0.490138161],_ +[0.52,0.499028444,asinh(0.52),asinh(0.52)-0.499028444],_ +[0.53,0.507882413,asinh(0.53),asinh(0.53)-0.507882413],_ +[0.54,0.516699824,asinh(0.54),asinh(0.54)-0.516699824],_ +[0.55,0.525480448,asinh(0.55),asinh(0.55)-0.525480448],_ +[0.56,0.534224074,asinh(0.56),asinh(0.56)-0.534224074],_ +[0.57,0.542930505,asinh(0.57),asinh(0.57)-0.542930505],_ +[0.58,0.551599562,asinh(0.58),asinh(0.58)-0.551599562],_ +[0.59,0.560231077,asinh(0.59),asinh(0.59)-0.560231077],_ +[0.60,0.568824899,asinh(0.60),asinh(0.60)-0.568824899],_ +[0.61,0.577380892,asinh(0.61),asinh(0.61)-0.577380892],_ +[0.62,0.585898932,asinh(0.62),asinh(0.62)-0.585898932],_ +[0.63,0.594378911,asinh(0.63),asinh(0.63)-0.594378911],_ +[0.64,0.602820733,asinh(0.64),asinh(0.64)-0.602820733],_ +[0.65,0.611224314,asinh(0.65),asinh(0.65)-0.611224314],_ +[0.66,0.619589584,asinh(0.66),asinh(0.66)-0.619589584],_ +[0.67,0.627916485,asinh(0.67),asinh(0.67)-0.627916485],_ +[0.68,0.636204970,asinh(0.68),asinh(0.68)-0.636204970],_ +[0.69,0.644455005,asinh(0.69),asinh(0.69)-0.644455005],_ +[0.70,0.652666566,asinh(0.70),asinh(0.70)-0.652666566],_ +[0.71,0.660839641,asinh(0.71),asinh(0.71)-0.660839641],_ +[0.72,0.668974227,asinh(0.72),asinh(0.72)-0.668974227],_ +[0.73,0.677070332,asinh(0.73),asinh(0.73)-0.677070332],_ +[0.74,0.685127974,asinh(0.74),asinh(0.74)-0.685127974],_ +[0.75,0.693147181,asinh(0.75),asinh(0.75)-0.693147181],_ +[0.76,0.701127988,asinh(0.76),asinh(0.76)-0.701127988],_ +[0.77,0.709070441,asinh(0.77),asinh(0.77)-0.709070441],_ +[0.78,0.716974594,asinh(0.78),asinh(0.78)-0.716974594],_ +[0.79,0.724840509,asinh(0.79),asinh(0.79)-0.724840509],_ +[0.80,0.732668256,asinh(0.80),asinh(0.80)-0.732668256],_ +[0.81,0.740457912,asinh(0.81),asinh(0.81)-0.740457912],_ +[0.82,0.748209563,asinh(0.82),asinh(0.82)-0.748209563],_ +[0.83,0.755923300,asinh(0.83),asinh(0.83)-0.755923300],_ +[0.84,0.763599222,asinh(0.84),asinh(0.84)-0.763599222],_ +[0.85,0.771237433,asinh(0.85),asinh(0.85)-0.771237433],_ +[0.86,0.778838046,asinh(0.86),asinh(0.86)-0.778838046],_ +[0.87,0.786401177,asinh(0.87),asinh(0.87)-0.786401177],_ +[0.88,0.793926950,asinh(0.88),asinh(0.88)-0.793926950],_ +[0.89,0.801415491,asinh(0.89),asinh(0.89)-0.801415491],_ +[0.90,0.808866936,asinh(0.90),asinh(0.90)-0.808866936],_ +[0.91,0.816281421,asinh(0.91),asinh(0.91)-0.816281421],_ +[0.92,0.823659091,asinh(0.92),asinh(0.92)-0.823659091],_ +[0.93,0.831000091,asinh(0.93),asinh(0.93)-0.831000091],_ +[0.94,0.838304575,asinh(0.94),asinh(0.94)-0.838304575],_ +[0.95,0.845572697,asinh(0.95),asinh(0.95)-0.845572697],_ +[0.96,0.852804617,asinh(0.96),asinh(0.96)-0.852804617],_ +[0.97,0.860000498,asinh(0.97),asinh(0.97)-0.860000498],_ +[0.98,0.867160507,asinh(0.98),asinh(0.98)-0.867160507],_ +[0.99,0.874284812,asinh(0.99),asinh(0.99)-0.874284812],_ +[1.00,0.881373587,asinh(1.00),asinh(1.00)-0.881373587]] +--R +--R +--R (1) +--R [[0.0,0.0,0.0,0.0], +--R [0.01,0.009999833,0.0099998333 4083288693 52,0.3408328869 35 E -9], +--R [0.02,0.019998667,0.0199986669 0660953936,- 0.9339046064 E -10], +--R [0.03,0.029995502,0.0299955018 2152425832 6,- 0.1784757416 74 E -9], +--R [0.04,0.039989341,0.0399893410 0602700269 1,0.6027002691 E -11], +--R [0.05,0.04997919,0.0499791900 6934866523 2,0.6934866523 2 E -10], +--R [0.06,0.059964058,0.0599640581 9533394203 3,0.1953339420 3 E -9], +--R [0.07,0.069942959,0.0699429590 1940182241 9,0.1940182242 E -10], +--R [0.08,0.079914912,0.0799149114 9449676816 5,- 0.5055032318 35 E -9], +--R [0.09,0.089878941,0.0898789407 4394680193 8,- 0.2560531980 6 E -9], +--R [0.1,0.099834079,0.0998340788 9920756332 7,- 0.1007924366 7 E -9], +--R [0.11,0.109779366,0.1097793659 2054342078,- 0.7945657921 7 E -10], +--R [0.12,0.119713851,0.1197138503 9877738636,- 0.6012226136 36 E -9], +--R [0.13,0.12963659,0.1296365903 3633024308,0.3363302430 8 E -9], +--R [0.14,0.139546654,0.1395466539 0586528422,- 0.9413471578 E -10], +--R [0.15,0.14944312,0.1494431201 8495765616,0.1849576561 6 E -9], +--R [0.16,0.15932508,0.1593250798 6531572882,- 0.1346842711 8 E -9], +--R [0.17,0.169191636,0.1691916359 3519539889,- 0.6480460111 E -10], +--R [0.18,0.179041904,0.1790419043 3376594692,0.3337659469 2 E -9], +--R [0.19,0.188875015,0.1888750145 7630719416,- 0.4236928058 4 E -9], +--R [0.2,0.19869011,0.1986901103 4924140647,0.3492414064 7 E -9], +--R [0.21,0.20848635,0.2084863500 7412884481,0.7412884481 E -10], +--R [0.22,0.218262908,0.2182629074 3988224632,- 0.5601177536 8 E -9], +--R [0.23,0.228018972,0.2280189719 0258204081,- 0.9741795919 E -10], +--R [0.24,0.237753749,0.2377537491 5239999115,0.1523999911 5 E -9], +--R [0.25,0.247466462,0.2474664615 4726345294,- 0.4527365470 6 E -9], +--R [0.26,0.257156349,0.2571563485 1301487614,- 0.4869851238 6 E -9], +--R [0.27,0.266822667,0.2668226669 0994085825,- 0.9005914175 E -10], +--R [0.28,0.276464691,0.2764646913 6566139339,0.3656613933 9 E -9], +--R [0.29,0.286081715,0.2860817145 7448237948,- 0.4255176205 2 E -9], +--R [0.3,0.295673048,0.2956730475 634224391,- 0.4365775609 E -9], +--R [0.31,0.30523802,0.3052380199 2522822388,- 0.7477177612 E -10], +--R [0.32,0.31477598,0.3147759800 1879020946,0.187902095 E -10], +--R [0.33,0.324286295,0.3242862951 3746321043,0.1374632104 E -9], +--R [0.34,0.333768352,0.3337683516 4588216777,- 0.3541178322 3 E -9], +--R [0.35,0.343221555,0.3432215550 8594396213,0.8594396213 E -10], +--R [0.36,0.35264533,0.3526453302 5269991354,0.2526999135 4 E -9], +--R [0.37,0.362039121,0.3620391212 4097112736,0.2409711273 6 E -9], +--R [0.38,0.371402391,0.3714023914 6355987334,0.4635598733 4 E -9], +--R [0.39,0.380734624,0.3807346236 4198472547,- 0.3580152745 3 E -9], +--R [0.4,0.39003532,0.3900353197 7071527608,- 0.2292847239 E -9], +--R [0.41,0.399304001,0.3993040010 5592394477,0.5592394477 E -10], +--R [0.42,0.408540208,0.4085402078 298078441,- 0.1701921559 E -9], +--R [0.43,0.4177435,0.4177434994 4156299241,- 0.5584370075 9 E -9], +--R [0.44,0.426913454,0.4269134541 2611656164,0.1261165616 E -9], +--R [0.45,0.436049669,0.4360496688 517405265,- 0.1482594735 E -9], +--R [0.46,0.445151759,0.4451517591 4768227909,0.1476822791 E -9], +--R [0.47,0.454219359,0.4542193589 1295474595,- 0.8704525405 E -10], +--R [0.48,0.46325212,0.4632521202 0743057053,0.2074305705 E -9], +--R [0.49,0.472249713,0.4722497130 2638229031,0.263822903 E -10], +--R [0.5,0.481211825,0.4812118250 596034475,0.596034475 E -10], +--R [0.51,0.490138161,0.4901381614 3623452983,0.4362345298 3 E -9], +--R [0.52,0.499028444,0.4990284444 564028591,0.4564028591 E -9], +--R [0.53,0.507882413,0.5078824133 1076734063,0.3107673406 E -9], +--R [0.54,0.516699824,0.5166998237 890376715,- 0.2109623285 E -9], +--R [0.55,0.525480448,0.5254804479 7851348895,- 0.214865111 E -10], +--R [0.56,0.534224074,0.5342240739 5366232528,- 0.463376747 E -10], +--R [0.57,0.542930505,0.5429305054 5772642154,0.4577264215 E -9], +--R [0.58,0.551599562,0.5515995615 7731772498,- 0.422682275 E -9], +--R [0.59,0.560231077,0.5602310764 1092803468,- 0.5890719653 2 E -9], +--R [0.6,0.568824899,0.5688248987 322475301,- 0.2677524699 E -9], +--R [0.61,0.577380892,0.5773808916 4915007492,- 0.3508499251 E -9], +--R [0.62,0.585898932,0.5858989322 5916797142,0.2591679714 E -9], +--R [0.63,0.594378911,0.5943789113 0224247799,0.302242478 E -9], +--R [0.64,0.602820733,0.6028207328 1149960517,- 0.1885003948 E -9], +--R [0.65,0.611224314,0.6112243137 62763672,- 0.237236328 E -9], +--R [0.66,0.619589584,0.6195895837 234840191,- 0.2765159809 E -9], +--R [0.67,0.627916485,0.6279164845 0171330467,- 0.4982866953 3 E -9], +--R [0.68,0.63620497,0.6362049697 9573911039,- 0.2042608896 E -9], +--R [0.69,0.644455005,0.6444550048 449342957,- 0.1550657043 E -9], +--R [0.7,0.652666566,0.6526665660 8235578681,0.8235578681 E -10], +--R [0.71,0.660839641,0.6608396407 8958638519,- 0.2104136148 E -9], +--R [0.72,0.668974227,0.6689742267 542798277,- 0.2457201723 E -9], +--R [0.73,0.677070332,0.6770703319 3083581572,- 0.6916418427 E -10], +--R [0.74,0.685127974,0.6851279741 0459912826,0.1045991283 E -9], +--R [0.75,0.693147181,0.6931471805 5994530942,- 0.4400546906 E -9], +--R [0.76,0.701127988,0.7011279877 5258482712,- 0.2474151729 E -9], +--R [0.77,0.709070441,0.7090704409 8638808148,- 0.136119185 E -10], +--R [0.78,0.716974594,0.7169745940 9500523361,0.9500523361 E -10], +--R [0.79,0.724840509,0.7248405091 2852755291,0.1285275529 E -9], +--R [0.8,0.732668256,0.7326682560 4541086415,0.454108642 E -10], +--R [0.81,0.740457912,0.7404579124 098567228,0.4098567228 E -9], +--R [0.82,0.748209563,0.7482095630 9482316487,0.9482316487 E -10], +--R [0.83,0.7559233,0.7559232999 9081426309,- 0.918573691 E -11], +--R [0.84,0.763599222,0.7635992217 205762674,- 0.2794237326 E -9], +--R [0.85,0.771237433,0.7712374333 5980780282,0.3598078028 E -9], +--R [0.86,0.778838046,0.7788380461 6397242546,0.1639724255 E -9], +--R [0.87,0.786401177,0.7864011773 0128377712,0.3012837771 E -9], +--R [0.88,0.79392695,0.7939269495 9191660771,- 0.4080833923 E -9], +--R [0.89,0.801415491,0.8014154912 5348102582,0.2534810258 E -9], +--R [0.9,0.808866936,0.8088669356 5278246251,- 0.3472175375 E -9], +--R [0.91,0.816281421,0.8162814210 6387596132,0.6387596132 E -10], +--R [0.92,0.823659091,0.8236590904 3241050549,- 0.5675894945 2 E -9], +--R [0.93,0.831000091,0.8310000911 4624712798,0.146247128 E -9], +--R [0.94,0.838304575,0.8383045748 1232348677,- 0.1876765132 E -9], +--R [0.95,0.845572697,0.8455726970 3972738992,0.397273899 E -10], +--R [0.96,0.852804617,0.8528046172 2893238837,0.2289323884 E -9], +--R [0.97,0.860000498,0.8600004983 6713998068,0.3671399807 E -9], +--R [0.98,0.867160507,0.8671605068 2966515846,- 0.1703348415 E -9], +--R [0.99,0.874284812,0.8742848121 8729492676,0.1872949268 E -9], +--R [1.0,0.881373587,0.8813735870 1954302523,0.195430252 E -10]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of atanh, ranging from 0.01 to 0.99. The +second column is the reference value of atanh from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp221 + +<<*>>= +--S 2 of 2 +[[0.00,0.000000000,atanh(0.00),atanh(0.00)-0.000000000],_ +[0.01,0.010000333,atanh(0.01),atanh(0.01)-0.010000333],_ +[0.02,0.020002667,atanh(0.02),atanh(0.02)-0.020002667],_ +[0.03,0.030009004,atanh(0.03),atanh(0.03)-0.030009004],_ +[0.04,0.040021353,atanh(0.04),atanh(0.04)-0.040021353],_ +[0.05,0.050041729,atanh(0.05),atanh(0.05)-0.050041729],_ +[0.06,0.060072156,atanh(0.06),atanh(0.06)-0.060072156],_ +[0.07,0.070114671,atanh(0.07),atanh(0.07)-0.070114671],_ +[0.08,0.080171325,atanh(0.08),atanh(0.08)-0.080171325],_ +[0.09,0.090244188,atanh(0.09),atanh(0.09)-0.090244188],_ +[0.10,0.100335347,atanh(0.10),atanh(0.10)-0.100335347],_ +[0.11,0.110446915,atanh(0.11),atanh(0.11)-0.110446915],_ +[0.12,0.120581028,atanh(0.12),atanh(0.12)-0.120581028],_ +[0.13,0.130739850,atanh(0.13),atanh(0.13)-0.130739850],_ +[0.14,0.140925576,atanh(0.14),atanh(0.14)-0.140925576],_ +[0.15,0.151140436,atanh(0.15),atanh(0.15)-0.151140436],_ +[0.16,0.161386696,atanh(0.16),atanh(0.16)-0.161386696],_ +[0.17,0.171666663,atanh(0.17),atanh(0.17)-0.171666663],_ +[0.18,0.181982689,atanh(0.18),atanh(0.18)-0.181982689],_ +[0.19,0.192337169,atanh(0.19),atanh(0.19)-0.192337169],_ +[0.20,0.202732554,atanh(0.20),atanh(0.20)-0.202732554],_ +[0.21,0.213171346,atanh(0.21),atanh(0.21)-0.213171346],_ +[0.22,0.223656109,atanh(0.22),atanh(0.22)-0.223656109],_ +[0.23,0.234189466,atanh(0.23),atanh(0.23)-0.234189466],_ +[0.24,0.244774112,atanh(0.24),atanh(0.24)-0.244774112],_ +[0.25,0.255412812,atanh(0.25),atanh(0.25)-0.255412812],_ +[0.26,0.266108407,atanh(0.26),atanh(0.26)-0.266108407],_ +[0.27,0.276863823,atanh(0.27),atanh(0.27)-0.276863823],_ +[0.28,0.287682072,atanh(0.28),atanh(0.28)-0.287682072],_ +[0.29,0.298566264,atanh(0.29),atanh(0.29)-0.298566264],_ +[0.30,0.309519604,atanh(0.30),atanh(0.30)-0.309519604],_ +[0.31,0.320545409,atanh(0.31),atanh(0.31)-0.320545409],_ +[0.32,0.331647108,atanh(0.32),atanh(0.32)-0.331647108],_ +[0.33,0.342828254,atanh(0.33),atanh(0.33)-0.342828254],_ +[0.34,0.354092528,atanh(0.34),atanh(0.34)-0.354092528],_ +[0.35,0.365443754,atanh(0.35),atanh(0.35)-0.365443754],_ +[0.36,0.376885901,atanh(0.36),atanh(0.36)-0.376885901],_ +[0.37,0.388423100,atanh(0.37),atanh(0.37)-0.388423100],_ +[0.38,0.400059650,atanh(0.38),atanh(0.38)-0.400059650],_ +[0.39,0.411800034,atanh(0.39),atanh(0.39)-0.411800034],_ +[0.40,0.423648930,atanh(0.40),atanh(0.40)-0.423648930],_ +[0.41,0.435611223,atanh(0.41),atanh(0.41)-0.435611223],_ +[0.42,0.447692023,atanh(0.42),atanh(0.42)-0.447692023],_ +[0.43,0.459896681,atanh(0.43),atanh(0.43)-0.459896681],_ +[0.44,0.472230804,atanh(0.44),atanh(0.44)-0.472230804],_ +[0.45,0.484700279,atanh(0.45),atanh(0.45)-0.484700279],_ +[0.46,0.497311288,atanh(0.46),atanh(0.46)-0.497311288],_ +[0.47,0.510070337,atanh(0.47),atanh(0.47)-0.510070337],_ +[0.48,0.522984278,atanh(0.48),atanh(0.48)-0.522984278],_ +[0.49,0.536060337,atanh(0.49),atanh(0.49)-0.536060337],_ +[0.50,0.549306144,atanh(0.50),atanh(0.50)-0.549306144],_ +[0.51,0.562729769,atanh(0.51),atanh(0.51)-0.562729769],_ +[0.52,0.576339754,atanh(0.52),atanh(0.52)-0.576339754],_ +[0.53,0.590145160,atanh(0.53),atanh(0.53)-0.590145160],_ +[0.54,0.604155603,atanh(0.54),atanh(0.54)-0.604155603],_ +[0.55,0.618381313,atanh(0.55),atanh(0.55)-0.618381313],_ +[0.56,0.632833186,atanh(0.56),atanh(0.56)-0.632833186],_ +[0.57,0.647522844,atanh(0.57),atanh(0.57)-0.647522844],_ +[0.58,0.662462707,atanh(0.58),atanh(0.58)-0.662462707],_ +[0.59,0.677666068,atanh(0.59),atanh(0.59)-0.677666068],_ +[0.60,0.693147180,atanh(0.60),atanh(0.60)-0.693147180],_ +[0.61,0.708921359,atanh(0.61),atanh(0.61)-0.708921359],_ +[0.62,0.725005087,atanh(0.62),atanh(0.62)-0.725005087],_ +[0.63,0.741416144,atanh(0.63),atanh(0.63)-0.741416144],_ +[0.64,0.758173745,atanh(0.64),atanh(0.64)-0.758173745],_ +[0.65,0.775298706,atanh(0.65),atanh(0.65)-0.775298706],_ +[0.66,0.792813631,atanh(0.66),atanh(0.66)-0.792813631],_ +[0.67,0.810743125,atanh(0.67),atanh(0.67)-0.810743125],_ +[0.68,0.829114038,atanh(0.68),atanh(0.68)-0.829114038],_ +[0.69,0.847955755,atanh(0.69),atanh(0.69)-0.847955755],_ +[0.70,0.867300527,atanh(0.70),atanh(0.70)-0.867300527],_ +[0.71,0.887183863,atanh(0.71),atanh(0.71)-0.887183863],_ +[0.72,0.907644983,atanh(0.72),atanh(0.72)-0.907644983],_ +[0.73,0.928727364,atanh(0.73),atanh(0.73)-0.928727364],_ +[0.74,0.950479381,atanh(0.74),atanh(0.74)-0.950479381],_ +[0.75,0.972955074,atanh(0.75),atanh(0.75)-0.972955074],_ +[0.76,0.996215082,atanh(0.76),atanh(0.76)-0.996215082],_ +[0.77,1.020327758,atanh(0.77),atanh(0.77)-1.020327758],_ +[0.78,1.045370548,atanh(0.78),atanh(0.78)-1.045370548],_ +[0.79,1.071431684,atanh(0.79),atanh(0.79)-1.071431684],_ +[0.80,1.098612289,atanh(0.80),atanh(0.80)-1.098612289],_ +[0.81,1.127029026,atanh(0.81),atanh(0.81)-1.127029026],_ +[0.82,1.156817465,atanh(0.82),atanh(0.82)-1.156817465],_ +[0.83,1.188136404,atanh(0.83),atanh(0.83)-1.188136404],_ +[0.84,1.221173518,atanh(0.84),atanh(0.84)-1.221173518],_ +[0.85,1.256152811,atanh(0.85),atanh(0.85)-1.256152811],_ +[0.86,1.293344672,atanh(0.86),atanh(0.86)-1.293344672],_ +[0.87,1.333079629,atanh(0.87),atanh(0.87)-1.333079629],_ +[0.88,1.375767657,atanh(0.88),atanh(0.88)-1.375767657],_ +[0.89,1.421925871,atanh(0.89),atanh(0.89)-1.421925871],_ +[0.90,1.472219490,atanh(0.90),atanh(0.90)-1.472219490],_ +[0.91,1.527524425,atanh(0.91),atanh(0.91)-1.527524425],_ +[0.92,1.589026915,atanh(0.92),atanh(0.92)-1.589026915],_ +[0.93,1.658390020,atanh(0.93),atanh(0.93)-1.658390020],_ +[0.94,1.738049345,atanh(0.94),atanh(0.94)-1.738049345],_ +[0.95,1.831780823,atanh(0.95),atanh(0.95)-1.831780823],_ +[0.96,1.945910149,atanh(0.96),atanh(0.96)-1.945910149],_ +[0.97,2.092295720,atanh(0.97),atanh(0.97)-2.092295720],_ +[0.98,2.297559925,atanh(0.98),atanh(0.98)-2.297559925],_ +[0.99,2.646652412,atanh(0.99),atanh(0.99)-2.646652412]] +--R +--R +--R (2) +--R [[0.0,0.0,0.0,0.0], +--R [0.01,0.010000333,0.0100003333 5333476201 6,0.3533347620 16 E -9], +--R [0.02,0.020002667,0.0200026673 0684958071 7,0.3068495807 17 E -9], +--R [0.03,0.030009004,0.0300090048 6312647432 6,0.8631264743 26 E -9], +--R [0.04,0.040021353,0.0400213538 3676821291 2,0.8367682129 12 E -9], +--R [0.05,0.050041729,0.0500417292 7849126824 6,0.2784912682 46 E -9], +--R [0.06,0.060072156,0.0600721559 2103162366 2,- 0.7896837633 8 E -10], +--R [0.07,0.070114671,0.0701146706 5432511799,- 0.3456748820 1 E -9], +--R [0.08,0.080171325,0.0801713250 3758969169,0.3758969169 E -10], +--R [0.09,0.090244188,0.0902441878 5614682960 9,- 0.1438531703 9 E -9], +--R [0.1,0.100335347,0.1003353477 3107558064,0.7310755806 36 E -9], +--R [0.11,0.110446915,0.1104469157 9009714872,0.7900971487 22 E -9], +--R [0.12,0.120581028,0.1205810284 0844403523,0.4084440352 3 E -9], +--R [0.13,0.13073985,0.1307398500 28878425,0.28878425 E -10], +--R [0.14,0.140925576,0.1409255760 7049386396,0.7049386396 E -10], +--R [0.15,0.151140436,0.1511404359 3646680528,- 0.6353319472 E -10], +--R [0.16,0.161386696,0.1613866961 3152551534,0.1315255153 4 E -9], +--R [0.17,0.171666663,0.1716666635 0057909768,0.5005790976 8 E -9], +--R [0.18,0.181982689,0.1819826886 0070582337,- 0.3992941766 3 E -9], +--R [0.19,0.192337169,0.1923371692 1954530989,0.2195453098 9 E -9], +--R [0.2,0.202732554,0.2027325540 5408219099,0.5408219099 E -10], +--R [0.21,0.213171346,0.2131713465 6485979698,0.5648597969 8 E -9], +--R [0.22,0.223656109,0.2236561090 2183241065,0.2183241065 E -10], +--R [0.23,0.234189466,0.2341894667 5936682305,0.7593668230 5 E -9], +--R [0.24,0.244774112,0.2447741126 5935289296,0.6593528929 6 E -9], +--R [0.25,0.255412812,0.2554128118 829953416,- 0.1170046584 E -9], +--R [0.26,0.266108407,0.2661084068 7365412176,- 0.1263458782 E -9], +--R [0.27,0.276863823,0.2768638226 5510007198,- 0.3448999280 2 E -9], +--R [0.28,0.287682072,0.2876820724 5178092744,0.4517809274 4 E -9], +--R [0.29,0.298566264,0.2985662636 6017834677,- 0.3398216532 3 E -9], +--R [0.3,0.309519604,0.3095196042 0311171547,0.2031117155 E -9], +--R [0.31,0.320545409,0.3205454093 0194608097,0.3019460809 7 E -9], +--R [0.32,0.331647108,0.3316471087 051320776,0.7051320776 E -9], +--R [0.33,0.342828254,0.3428282544 1539385272,0.4153938527 2 E -9], +--R [0.34,0.354092528,0.3540925289 6224291211,0.9622429121 E -9], +--R [0.35,0.365443754,0.3654437542 7139616907,0.2713961690 7 E -9], +--R [0.36,0.376885901,0.3768859011 88190076,0.188190076 E -9], +--R [0.37,0.3884231,0.3884230997 1829611371,- 0.2817038862 9 E -9], +--R [0.38,0.40005965,0.4000596500 5605656814,0.5605656814 E -10], +--R [0.39,0.411800034,0.4118000344 7869025422,0.4786902542 2 E -9], +--R [0.4,0.42364893,0.4236489301 9360180685,0.1936018069 E -9], +--R [0.41,0.435611223,0.4356112232 362244138,0.2362244138 E -9], +--R [0.42,0.447692023,0.4476920235 2742069707,0.5274206970 7 E -9], +--R [0.43,0.459896681,0.4598966812 1267856435,0.2126785644 E -9], +--R [0.44,0.472230804,0.4722308044 2042569355,0.4204256935 5 E -9], +--R [0.45,0.484700279,0.4847002785 9405174156,- 0.4059482584 4 E -9], +--R [0.46,0.497311288,0.4973112875 7203102745,- 0.4279689725 5 E -9], +--R [0.47,0.510070337,0.5100703366 1330723373,- 0.3866927663 E -9], +--R [0.48,0.522984278,0.5229842775 9134385416,- 0.4086561458 E -9], +--R [0.49,0.536060337,0.5360603366 1056668467,- 0.3894333153 E -9], +--R [0.5,0.549306144,0.5493061443 340548457,0.3340548457 E -9], +--R [0.51,0.562729769,0.5627297693 521488593,0.3521488593 E -9], +--R [0.52,0.576339754,0.5763397549 691927296,0.9691927296 E -9], +--R [0.53,0.59014516,0.5901451598 4118843811,- 0.1588115619 E -9], +--R [0.54,0.604155603,0.6041556029 6226707918,- 0.377329208 E -10], +--R [0.55,0.618381313,0.6183813135 7446343157,0.5744634315 7 E -9], +--R [0.56,0.632833186,0.6328331866 6563794169,0.6656379416 9 E -9], +--R [0.57,0.647522844,0.6475228448 2737281698,0.8273728169 8 E -9], +--R [0.58,0.662462707,0.6624627073 7179924883,0.3717992488 E -9], +--R [0.59,0.677666068,0.6776660677 5796186084,- 0.2420381392 E -9], +--R [0.6,0.69314718,0.6931471805 5994530942,0.5599453094 2 E -9], +--R [0.61,0.708921359,0.7089213594 2740828423,0.4274082842 E -9], +--R [0.62,0.725005087,0.7250050877 5299915279,0.7529991527 9 E -9], +--R [0.63,0.741416144,0.7414161440 8126894485,0.8126894484 E -10], +--R [0.64,0.758173745,0.7581737446 8404421054,- 0.3159557895 E -9], +--R [0.65,0.775298706,0.7752987062 0558346517,0.2055834652 E -9], +--R [0.66,0.792813631,0.7928136318 7019092161,0.8701909216 1 E -9], +--R [0.67,0.810743125,0.8107431254 7513743591,0.4751374359 1 E -9], +--R [0.68,0.829114038,0.8291140383 0176618883,0.3017661888 E -9], +--R [0.69,0.847955755,0.8479557552 1896361309,0.2189636131 E -9], +--R [0.7,0.867300527,0.8673005276 9405319443,0.6940531944 3 E -9], +--R [0.71,0.887183863,0.8871838632 5809290781,0.2580929078 E -9], +--R [0.72,0.907644983,0.9076449833 1912455918,0.3191245592 E -9], +--R [0.73,0.928727364,0.9287273642 4672493638,0.2467249364 E -9], +--R [0.74,0.950479381,0.9504793805 9652349126,- 0.4034765087 E -9], +--R [0.75,0.972955074,0.9729550745 2765665255,0.5276566525 5 E -9], +--R [0.76,0.996215082,0.9962150823 4510308105,0.345103081 E -9], +--R [0.77,1.020327758,1.0203277583 223397256,0.3223397256 E -9], +--R [0.78,1.045370548,1.0453705484 668846471,0.4668846471 E -9], +--R [0.79,1.071431684,1.0714316840 586659998,0.586659998 E -10], +--R [0.8,1.098612289,1.0986122886 681096914,- 0.3318903086 E -9], +--R [0.81,1.127029026,1.1270290260 496926434,0.496926434 E -10], +--R [0.82,1.156817465,1.1568174645 903153292,- 0.4096846708 E -9], +--R [0.83,1.188136404,1.1881364043 926024299,0.3926024299 E -9], +--R [0.84,1.221173518,1.2211735176 846021907,- 0.3153978093 E -9], +--R [0.85,1.256152811,1.2561528119 880573765,0.9880573764 9 E -9], +--R [0.86,1.293344672,1.2933446720 489713161,0.489713161 E -10], +--R [0.87,1.333079629,1.3330796296 965249441,0.6965249441 E -9], +--R [0.88,1.375767657,1.3757676565 209744477,- 0.4790255523 E -9], +--R [0.89,1.421925871,1.4219258711 306359176,0.1306359176 E -9], +--R [0.9,1.47221949,1.4722194895 8322023,- 0.41677977 E -9], +--R [0.91,1.527524425,1.5275244253 55205245,0.355205245 E -9], +--R [0.92,1.589026915,1.5890269151 739728098,0.1739728098 E -9], +--R [0.93,1.65839002,1.6583900199 247861234,- 0.752138766 E -10], +--R [0.94,1.738049345,1.7380493449 176365654,- 0.823634346 E -10], +--R [0.95,1.831780823,1.8317808230 648232137,0.648232137 E -10], +--R [0.96,1.945910149,1.9459101490 553133051,0.553133051 E -10], +--R [0.97,2.09229572,2.0922957200 349394077,0.349394077 E -10], +--R [0.98,2.297559925,2.2975599250 672949634,0.672949634 E -10], +--R [0.99,2.646652412,2.6466524123 622461976,0.3622461976 E -9]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ + +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf Digital Library of Mathematical Functions}, +http://dlmf.nist.gov +\bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp221 +\end{thebibliography} +\end{document} diff --git a/src/input/besselk.input.pamphlet b/src/input/besselk.input.pamphlet index 0cd01ea..7a31a2c 100644 --- a/src/input/besselk.input.pamphlet +++ b/src/input/besselk.input.pamphlet @@ -9,6 +9,11 @@ \eject \tableofcontents \eject +In the following table there are 4 columns. The first column +is the argument of besselK, ranging from 0.01 to 10.0. The +second column is the reference value of Gamma from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp417-419 <<*>>= )spool besselk.output )set message test on @@ -45,13 +50,122 @@ limit(D(besselK(a,x),a),a=1/2) --R (4) "failed" --R Type: Union("failed",...) --E 4 + +--S 5 +stegun(x)== %e^x * besselK(1,x) +--E 5 + +--S 6 +[[0.1, 10.890182683 , stegun(0.1), stegun(0.1)- 10.890182683 ],_ + [0.2, 5.833386037 , stegun(0.2), stegun(0.2)- 5.833386037 ],_ + [0.3, 4.125157762 , stegun(0.3), stegun(0.3)- 4.125157762 ],_ + [0.4, 3.258673880 , stegun(0.4), stegun(0.4)- 3.258673880 ],_ + [0.5, 2.7310097082, stegun(0.5), stegun(0.5)- 2.7310097082],_ + [0.6, 2.3739200376, stegun(0.6), stegun(0.6)- 2.3739200376],_ + [0.7, 2.1150113128, stegun(0.7), stegun(0.7)- 2.1150113128],_ + [0.8, 1.9179302990, stegun(0.8), stegun(0.8)- 1.9179302990],_ + [0.9, 1.7623882197, stegun(0.9), stegun(0.9)- 1.7623882197],_ + [1.0, 1.6361534863, stegun(1.0), stegun(1.0)- 1.6361534863],_ + [1.1, 1.5314037541, stegun(1.1), stegun(1.1)- 1.5314037541],_ + [1.2, 1.4428975522, stegun(1.2), stegun(1.2)- 1.4428975522],_ + [1.3, 1.3669872841, stegun(1.3), stegun(1.3)- 1.3669872841],_ + [1.4, 1.3010537400, stegun(1.4), stegun(1.4)- 1.3010537400],_ + [1.5, 1.2431658736, stegun(1.5), stegun(1.5)- 1.2431658736],_ + [1.6, 1.1918675654, stegun(1.6), stegun(1.6)- 1.1918675654],_ + [1.7, 1.1460392462, stegun(1.7), stegun(1.7)- 1.1460392462],_ + [1.8, 1.1048053726, stegun(1.8), stegun(1.8)- 1.1048053726],_ + [1.9, 1.0674709298, stegun(1.9), stegun(1.9)- 1.0674709298],_ + [2.0, 1.0334768471, stegun(2.0), stegun(2.0)- 1.0334768471],_ + [2.1, 1.0023680527, stegun(2.1), stegun(2.1)- 1.0023680527],_ + [2.2, 0.9737701679, stegun(2.2), stegun(2.2)- 0.9737701679],_ + [2.3, 0.9473722250, stegun(2.3), stegun(2.3)- 0.9473722250],_ + [2.4, 0.9229136650, stegun(2.4), stegun(2.4)- 0.9229136650],_ + [2.5, 0.9001744239, stegun(2.5), stegun(2.5)- 0.9001744239],_ + [2.6, 0.8789672806, stegun(2.6), stegun(2.6)- 0.8789672806],_ + [2.7, 0.8591318867, stegun(2.7), stegun(2.7)- 0.8591318867],_ + [2.8, 0.8405300604, stegun(2.8), stegun(2.8)- 0.8405300604],_ + [2.9, 0.8230420403, stegun(2.9), stegun(2.9)- 0.8230420403],_ + [3.0, 0.8065634800, stegun(3.0), stegun(3.0)- 0.8065634800],_ + [3.1, 0.7910030157, stegun(3.1), stegun(3.1)- 0.7910030157],_ + [3.2, 0.7762802824, stegun(3.2), stegun(3.2)- 0.7762802824],_ + [3.3, 0.7623242864, stegun(3.3), stegun(3.3)- 0.7623242864],_ + [3.4, 0.7490720613, stegun(3.4), stegun(3.4)- 0.7490720613],_ + [3.5, 0.7364675480, stegun(3.5), stegun(3.5)- 0.7364675480],_ + [3.6, 0.7244606608, stegun(3.6), stegun(3.6)- 0.7244606608],_ + [3.7, 0.7130065010, stegun(3.7), stegun(3.7)- 0.7130065010],_ + [3.8, 0.7020646931, stegun(3.8), stegun(3.8)- 0.7020646931],_ + [3.9, 0.6915988206, stegun(3.9), stegun(3.9)- 0.6915988206],_ + [4.0, 0.6815759452, stegun(4.0), stegun(4.0)- 0.6815759452],_ + [4.1, 0.6719661952, stegun(4.1), stegun(4.1)- 0.6719661952],_ + [4.2, 0.6627424110, stegun(4.2), stegun(4.2)- 0.6627424110],_ + [4.3, 0.6538798395, stegun(4.3), stegun(4.3)- 0.6538798395],_ + [4.4, 0.6453558689, stegun(4.4), stegun(4.4)- 0.6453558689],_ + [4.5, 0.6371497988, stegun(4.5), stegun(4.5)- 0.6371497988],_ + [4.6, 0.6292426383, stegun(4.6), stegun(4.6)- 0.6292426383],_ + [4.7, 0.6216169312, stegun(4.7), stegun(4.7)- 0.6216169312],_ + [4.8, 0.6142566003, stegun(4.8), stegun(4.8)- 0.6142566003],_ + [4.9, 0.6071468131, stegun(4.9), stegun(4.9)- 0.6071468131],_ + [5.0, 0.6002738587, stegun(5.0), stegun(5.0)- 0.6002738587],_ + [5.1, 0.5936250463, stegun(5.1), stegun(5.1)- 0.5936250463],_ + [5.2, 0.5871886062, stegun(5.2), stegun(5.2)- 0.5871886062],_ + [5.3, 0.5809536085, stegun(5.3), stegun(5.3)- 0.5809536085],_ + [5.4, 0.5749098871, stegun(5.4), stegun(5.4)- 0.5749098871],_ + [5.5, 0.5690479741, stegun(5.5), stegun(5.5)- 0.5690479741],_ + [5.6, 0.5633590393, stegun(5.6), stegun(5.6)- 0.5633590393],_ + [5.7, 0.5578348348, stegun(5.7), stegun(5.7)- 0.5578348348],_ + [5.8, 0.5524676495, stegun(5.8), stegun(5.8)- 0.5524676495],_ + [5.9, 0.5472502639, stegun(5.9), stegun(5.9)- 0.5472502639],_ + [6.0, 0.5421759104, stegun(6.0), stegun(6.0)- 0.5421759104],_ + [6.1, 0.5372382386, stegun(6.1), stegun(6.1)- 0.5372382386],_ + [6.2, 0.5324312833, stegun(6.2), stegun(6.2)- 0.5324312833],_ + [6.3, 0.5277494344, stegun(6.3), stegun(6.3)- 0.5277494344],_ + [6.4, 0.5231874101, stegun(6.4), stegun(6.4)- 0.5231874101],_ + [6.5, 0.5187402336, stegun(6.5), stegun(6.5)- 0.5187402336],_ + [6.6, 0.5144032108, stegun(6.6), stegun(6.6)- 0.5144032108],_ + [6.7, 0.5101719097, stegun(6.7), stegun(6.7)- 0.5101719097],_ + [6.8, 0.5060421421, stegun(6.8), stegun(6.8)- 0.5060421421],_ + [6.9, 0.5020099471, stegun(6.9), stegun(6.9)- 0.5020099471],_ + [7.0, 0.4980715749, stegun(7.0), stegun(7.0)- 0.4980715749],_ + [7.1, 0.4942234737, stegun(7.1), stegun(7.1)- 0.4942234737],_ + [7.2, 0.4904622755, stegun(7.2), stegun(7.2)- 0.4904622755],_ + [7.3, 0.4867847842, stegun(7.3), stegun(7.3)- 0.4867847842],_ + [7.4, 0.4831879648, stegun(7.4), stegun(7.4)- 0.4831879648],_ + [7.5, 0.4796689336, stegun(7.5), stegun(7.5)- 0.4796689336],_ + [7.6, 0.4762249486, stegun(7.6), stegun(7.6)- 0.4762249486],_ + [7.7, 0.4728533995, stegun(7.7), stegun(7.7)- 0.4728533995],_ + [7.8, 0.4695518010, stegun(7.8), stegun(7.8)- 0.4695518010],_ + [7.9, 0.4663177847, stegun(7.9), stegun(7.9)- 0.4663177847],_ + [8.0, 0.4631490928, stegun(8.0), stegun(8.0)- 0.4631490928],_ + [8.1, 0.4600435709, stegun(8.1), stegun(8.1)- 0.4600435709],_ + [8.2, 0.4569991615, stegun(8.2), stegun(8.2)- 0.4569991615],_ + [8.3, 0.4540139001, stegun(8.3), stegun(8.3)- 0.4540139001],_ + [8.4, 0.4510859089, stegun(8.4), stegun(8.4)- 0.4510859089],_ + [8.5, 0.4482133915, stegun(8.5), stegun(8.5)- 0.4482133915],_ + [8.6, 0.4453946295, stegun(8.6), stegun(8.6)- 0.4453946295],_ + [8.7, 0.4426279775, stegun(8.7), stegun(8.7)- 0.4426279775],_ + [8.8, 0.4399118594, stegun(8.8), stegun(8.8)- 0.4399118594],_ + [8.9, 0.4372447648, stegun(8.9), stegun(8.9)- 0.4372447648],_ + [9.0, 0.4346252454, stegun(9.0), stegun(9.0)- 0.4346252454],_ + [9.1, 0.4320519116, stegun(9.1), stegun(9.1)- 0.4320519116],_ + [9.2, 0.4295234301, stegun(9.2), stegun(9.2)- 0.4295234301],_ + [9.3, 0.4270385204, stegun(9.3), stegun(9.3)- 0.4270385204],_ + [9.4, 0.4245959520, stegun(9.4), stegun(9.4)- 0.4245959520],_ + [9.5, 0.4221945430, stegun(9.5), stegun(9.5)- 0.4221945430],_ + [9.6, 0.4198331565, stegun(9.6), stegun(9.6)- 0.4198331565],_ + [9.7, 0.4175106989, stegun(9.7), stegun(9.7)- 0.4175106989],_ + [9.8, 0.4152261179, stegun(9.8), stegun(9.8)- 0.4152261179],_ + [9.9, 0.4129784003, stegun(9.9), stegun(9.9)- 0.4129784003],_ + [10.0, 0.4107665704, stegun(10.0), stegun(10.0)- 0.4107665704]] +--E 6 + )spool )lisp (bye) @ \eject \begin{thebibliography}{99} -\bibitem{1} nothing +\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp417-419 \end{thebibliography} \end{document} diff --git a/src/input/exp.input.pamphlet b/src/input/exp.input.pamphlet new file mode 100644 index 0000000..88b3759 --- /dev/null +++ b/src/input/exp.input.pamphlet @@ -0,0 +1,460 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input exp.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This compares Axiom's exp function with the tables published in +Abramowitz and Stegun. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of exp(x), ranging from 0.0 to 10.0. The +second column is the reference value of exp from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp136-137 + +<<*>>= +)spool exp.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.0, 1.000000000000000, exp(0.0), exp(0.0)- 1.000000000000000],_ + [0.1, 1.105170918075648, exp(0.1), exp(0.1)- 1.105170918075648],_ + [0.2, 1.221402758160170, exp(0.2), exp(0.2)- 1.221402758160170],_ + [0.3, 1.349858807576003, exp(0.3), exp(0.3)- 1.349858807576003],_ + [0.4, 1.491824697641270, exp(0.4), exp(0.4)- 1.491824697641270],_ + [0.5, 1.648721270700128, exp(0.5), exp(0.5)- 1.648721270700128],_ + [0.6, 1.822118800390509, exp(0.6), exp(0.6)- 1.822118800390509],_ + [0.7, 2.013752707470477, exp(0.7), exp(0.7)- 2.013752707470477],_ + [0.8, 2.225540928492468, exp(0.8), exp(0.8)- 2.225540928492468],_ + [0.9, 2.459603111156950, exp(0.9), exp(0.9)- 2.459603111156950],_ + [1.0, 2.718281828459045, exp(1.0), exp(1.0)- 2.718281828459045],_ + [1.1, 3.004166023946433, exp(1.1), exp(1.1)- 3.004166023946433],_ + [1.2, 3.320116922736547, exp(1.2), exp(1.2)- 3.320116922736547],_ + [1.3, 3.669296667619244, exp(1.3), exp(1.3)- 3.669296667619244],_ + [1.4, 4.055199966844675, exp(1.4), exp(1.4)- 4.055199966844675],_ + [1.5, 4.481689070338065, exp(1.5), exp(1.5)- 4.481689070338065],_ + [1.6, 4.953032424395115, exp(1.6), exp(1.6)- 4.953032424395115],_ + [1.7, 5.473947391727200, exp(1.7), exp(1.7)- 5.473947391727200],_ + [1.8, 6.049647464412946, exp(1.8), exp(1.8)- 6.049647464412946],_ + [1.9, 6.685894442279269, exp(1.9), exp(1.9)- 6.685894442279269],_ + [2.0, 7.389056098930650, exp(2.0), exp(2.0)- 7.389056098930650],_ + [2.1, 8.166169912567650, exp(2.1), exp(2.1)- 8.166169912567650],_ + [2.2, 9.025013499434121, exp(2.2), exp(2.2)- 9.025013499434121],_ + [2.3, 9.974182454814721, exp(2.3), exp(2.3)- 9.974182454814721],_ + [2.4, 11.023176380641602, exp(2.4), exp(2.4)- 11.023176380641602],_ + [2.5, 12.182493960703473, exp(2.5), exp(2.5)- 12.182493960703473],_ + [2.6, 13.463738035001690, exp(2.6), exp(2.6)- 13.463738035001690],_ + [2.7, 14.879731724872834, exp(2.7), exp(2.7)- 14.879731724872834],_ + [2.8, 16.444646771097050, exp(2.8), exp(2.8)- 16.444646771097050],_ + [2.9, 18.174145369443061, exp(2.9), exp(2.9)- 18.174145369443061],_ + [3.0, 20.085536923187668, exp(3.0), exp(3.0)- 20.085536923187668],_ + [3.1, 22.197951281441633, exp(3.1), exp(3.1)- 22.197951281441633],_ + [3.2, 24.532530197109349, exp(3.2), exp(3.2)- 24.532530197109349],_ + [3.3, 27.112638920657887, exp(3.3), exp(3.3)- 27.112638920657887],_ + [3.4, 29.964100047397013, exp(3.4), exp(3.4)- 29.964100047397013],_ + [3.5, 33.115451958692314, exp(3.5), exp(3.5)- 33.115451958692314],_ + [3.6, 36.598234443677988, exp(3.6), exp(3.6)- 36.598234443677988],_ + [3.7, 40.447304360067391, exp(3.7), exp(3.7)- 40.447304360067391],_ + [3.8, 44.701184493300823, exp(3.8), exp(3.8)- 44.701184493300823],_ + [3.9, 49.402449105530174, exp(3.9), exp(3.9)- 49.402449105530174],_ + [4.0, 54.598150033144239, exp(4.0), exp(4.0)- 54.598150033144239],_ + [4.1, 60.340287597361969, exp(4.1), exp(4.1)- 60.340287597361969],_ + [4.2, 66.686331040925142, exp(4.2), exp(4.2)- 66.686331040925142],_ + [4.3, 73.699793699595797, exp(4.3), exp(4.3)- 73.699793699595797],_ + [4.4, 81.450868664968117, exp(4.4), exp(4.4)- 81.450868664968117],_ + [4.5, 90.017131300521814, exp(4.5), exp(4.5)- 90.017131300521814],_ + [4.6, 99.484315641933809, exp(4.6), exp(4.6)- 99.484315641933809],_ + [4.7, 109.947172452123499, exp(4.7), exp(4.7)- 109.947172452123499],_ + [4.8, 121.510417518734881, exp(4.8), exp(4.8)- 121.510417518734881],_ + [4.9, 134.289779684935485, exp(4.9), exp(4.9)- 134.289779684935485],_ + [5.0, 148.413159102577, exp(5.0), exp(5.0)- 148.413159102577],_ + [5.1, 164.021907299902, exp(5.1), exp(5.1)- 164.021907299902],_ + [5.2, 181.272241875151, exp(5.2), exp(5.2)- 181.272241875151],_ + [5.3, 200.336809974792, exp(5.3), exp(5.3)- 200.336809974792],_ + [5.4, 221.406416204187, exp(5.4), exp(5.4)- 221.406416204187],_ + [5.5, 244.691932264220, exp(5.5), exp(5.5)- 244.691932264220],_ + [5.6, 270.426407426153, exp(5.6), exp(5.6)- 270.426407426153],_ + [5.7, 298.867400967060, exp(5.7), exp(5.7)- 298.867400967060],_ + [5.8, 330.299559909649, exp(5.8), exp(5.8)- 330.299559909649],_ + [5.9, 365.037467865329, exp(5.9), exp(5.9)- 365.037467865329],_ + [6.0, 403.428793492735, exp(6.0), exp(6.0)- 403.428793492735],_ + [6.1, 445.857770082517, exp(6.1), exp(6.1)- 445.857770082517],_ + [6.2, 492.749041093256, exp(6.2), exp(6.2)- 492.749041093256],_ + [6.3, 544.571910125929, exp(6.3), exp(6.3)- 544.571910125929],_ + [6.4, 601.845037872082, exp(6.4), exp(6.4)- 601.845037872082],_ + [6.5, 665.141633044362, exp(6.5), exp(6.5)- 665.141633044362],_ + [6.6, 735.095189241973, exp(6.6), exp(6.6)- 735.095189241973],_ + [6.7, 812.405825167543, exp(6.7), exp(6.7)- 812.405825167543],_ + [6.8, 897.847291650418, exp(6.8), exp(6.8)- 897.847291650418],_ + [6.9, 992.274715605026, exp(6.9), exp(6.9)- 992.274715605026],_ + [7.0, 1096.633158428459, exp(7.0), exp(7.0)- 1096.633158428459],_ + [7.1, 1211.967074492577, exp(7.1), exp(7.1)- 1211.967074492577],_ + [7.2, 1339.430764394418, exp(7.2), exp(7.2)- 1339.430764394418],_ + [7.3, 1480.299927584545, exp(7.3), exp(7.3)- 1480.299927584545],_ + [7.4, 1635.984429995927, exp(7.4), exp(7.4)- 1635.984429995927],_ + [7.5, 1808.042414456063, exp(7.5), exp(7.5)- 1808.042414456063],_ + [7.6, 1998.195895104118, exp(7.6), exp(7.6)- 1998.195895104118],_ + [7.7, 2208.347991887209, exp(7.7), exp(7.7)- 2208.347991887209],_ + [7.8, 2440.601977624499, exp(7.8), exp(7.8)- 2440.601977624499],_ + [7.9, 2697.282328268509, exp(7.9), exp(7.9)- 2697.282328268509],_ + [8.0, 2980.957987041728, exp(8.0), exp(8.0)- 2980.957987041728],_ + [8.1, 3294.468075283841, exp(8.1), exp(8.1)- 3294.468075283841],_ + [8.2, 3640.950307332355, exp(8.2), exp(8.2)- 3640.950307332355],_ + [8.3, 4023.872393822310, exp(8.3), exp(8.3)- 4023.872393822310],_ + [8.4, 4447.066747699856, exp(8.4), exp(8.4)- 4447.066747699856],_ + [8.5, 4914.768840299134, exp(8.5), exp(8.5)- 4914.768840299134],_ + [8.6, 5431.659591362980, exp(8.6), exp(8.6)- 5431.659591362980],_ + [8.7, 6002.912217261022, exp(8.7), exp(8.7)- 6002.912217261022],_ + [8.8, 6634.244006277885, exp(8.8), exp(8.8)- 6634.244006277885],_ + [8.9, 7331.973539155993, exp(8.9), exp(8.9)- 7331.973539155993],_ + [9.0, 8103.083927575384, exp(9.0), exp(9.0)- 8103.083927575384],_ + [9.1, 8955.292703482512, exp(9.1), exp(9.1)- 8955.292703482512],_ + [9.2, 9897.129058743916, exp(9.2), exp(9.2)- 9897.129058743916],_ + [9.3, 10938.019208165184, exp(9.3), exp(9.3)- 10938.019208165184],_ + [9.4, 12088.380730216984, exp(9.4), exp(9.4)- 12088.380730216984],_ + [9.5, 13359.726829661872, exp(9.5), exp(9.5)- 13359.726829661872],_ + [9.6, 14764.781565577273, exp(9.6), exp(9.6)- 14764.781565577273],_ + [9.7, 16317.607198015432, exp(9.7), exp(9.7)- 16317.607198015432],_ + [9.8, 18033.744927828511, exp(9.8), exp(9.8)- 18033.744927828511],_ + [9.9, 19930.370438230289, exp(9.9), exp(9.9)- 19930.370438230289],_ +[10.0, 22026.465794806717, exp(10.0), exp(10.0)-22026.465794806717]] +--R +--R +--R (1) +--R [[0.0,1.0,1.0,0.0], +--R [0.1,1.1051709180 75648,1.1051709180 756476248,- 0.3752 E -15], +--R [0.2,1.2214027581 6017,1.2214027581 601698339,- 0.1661 E -15], +--R [0.3,1.3498588075 76003,1.3498588075 76003104,0.104 E -15], +--R [0.4,1.4918246976 4127,1.4918246976 412703178,0.3178 E -15], +--R [0.5,1.6487212707 00128,1.6487212707 001281468,0.1468 E -15], +--R [0.6,1.8221188003 90509,1.8221188003 905089749,- 0.251 E -16], +--R [0.7,2.0137527074 70477,2.0137527074 704765216,- 0.4784 E -15], +--R [0.8,2.2255409284 92468,2.2255409284 924676046,- 0.3954 E -15], +--R [0.9,2.4596031111 5695,2.4596031111 569496638,- 0.3362 E -15], +--R [1.0,2.7182818284 59045,2.7182818284 590452354,0.2354 E -15], +--R [1.1,3.0041660239 46433,3.0041660239 464331121,0.112 E -15], +--R [1.2,3.3201169227 36547,3.3201169227 365474895,0.4895 E -15], +--R [1.3,3.6692966676 19244,3.6692966676 192442204,0.22 E -15], +--R [1.4,4.0551999668 44675,4.0551999668 446745872,- 0.413 E -15], +--R [1.5,4.4816890703 38065,4.4816890703 380648226,- 0.177 E -15], +--R [1.6,4.9530324243 95115,4.9530324243 951148037,- 0.196 E -15], +--R [1.7,5.4739473917 272,5.4739473917 271997608,- 0.239 E -15], +--R [1.8,6.0496474644 12946,6.0496474644 129460837,0.837 E -16], +--R [1.9,6.6858944422 79269,6.6858944422 792694161,0.416 E -15], +--R [2.0,7.3890560989 3065,7.3890560989 306502272,0.227 E -15], +--R [2.1,8.1661699125 6765,8.1661699125 676500734,0.734 E -16], +--R [2.2,9.0250134994 34121,9.0250134994 341209265,- 0.735 E -16], +--R [2.3,9.9741824548 14721,9.9741824548 1472074,- 0.26 E -15], +--R [2.4,11.0231763806 41602,11.0231763806 41601652,- 0.348 E -15], +--R [2.5,12.1824939607 03473,12.1824939607 03473438,0.438 E -15], +--R [2.6,13.4637380350 0169,13.4637380350 01690398,0.398 E -15], +--R [2.7,14.8797317248 72834,14.8797317248 72834112,0.112 E -15], +--R [2.8,16.4446467710 9705,16.4446467710 97049871,- 0.129 E -15], +--R [2.9,18.1741453694 43061,18.1741453694 43060943,- 0.57 E -16], +--R [3.0,20.0855369231 87668,20.0855369231 87667741,- 0.259 E -15], +--R [3.1,22.1979512814 41633,22.1979512814 41633405,0.405 E -15], +--R [3.2,24.5325301971 09349,24.5325301971 09348644,- 0.356 E -15], +--R [3.3,27.1126389206 57887,27.1126389206 57887427,0.427 E -15], +--R [3.4,29.9641000473 97013,29.9641000473 97013348,0.348 E -15], +--R [3.5,33.1154519586 92314,33.1154519586 92313751,- 0.249 E -15], +--R [3.6,36.5982344436 77988,36.5982344436 77987752,- 0.248 E -15], +--R [3.7,40.4473043600 67391,40.4473043600 67390529,- 0.471 E -15], +--R [3.8,44.7011844933 00823,44.7011844933 00823038,0.38 E -16], +--R [3.9,49.4024491055 30174,49.4024491055 3017388,- 0.12 E -15], +--R [4.0,54.5981500331 44239,54.5981500331 44239078,0.78 E -16], +--R [4.1,60.3402875973 61969,60.3402875973 61969497,0.497 E -15], +--R [4.2,66.6863310409 25142,66.6863310409 25141644,- 0.36 E -15], +--R [4.3,73.6997936995 95797,73.6997936995 95796913,- 0.88 E -16], +--R [4.4,81.4508686649 68117,81.4508686649 68117445,0.445 E -15], +--R [4.5,90.0171313005 21814,90.0171313005 2181355,- 0.45 E -15], +--R [4.6,99.4843156419 33809,99.4843156419 33808735,- 0.26 E -15], +--R [4.7,109.9471724521 23499,109.9471724521 2349888,- 0.12 E -15], +--R [4.8,121.5104175187 34881,121.5104175187 3488076,- 0.24 E -15], +--R [4.9,134.2897796849 35485,134.2897796849 3548484,- 0.16 E -15], +--R [5.0,148.4131591025 77,148.4131591025 7660342,- 0.39658 E -12], +--R [5.1,164.0219072999 02,164.0219072999 0174394,- 0.25606 E -12], +--R [5.2,181.2722418751 51,181.2722418751 5117937,0.17937 E -12], +--R [5.3,200.3368099747 92,200.3368099747 9168484,- 0.31516 E -12], +--R [5.4,221.4064162041 87,221.4064162041 8708703,0.8703 E -13], +--R [5.5,244.6919322642 2,244.6919322642 2038792,0.38792 E -12], +--R [5.6,270.4264074261 53,270.4264074261 5262815,- 0.37185 E -12], +--R [5.7,298.8674009670 6,298.8674009670 6023267,0.23267 E -12], +--R [5.8,330.2995599096 49,330.2995599096 4865412,- 0.34588 E -12], +--R [5.9,365.0374678653 29,365.0374678653 2877732,- 0.2227 E -12], +--R [6.0,403.4287934927 35,403.4287934927 3512261,0.1226 E -12], +--R [6.1,445.8577700825 17,445.8577700825 1693179,- 0.6821 E -13], +--R [6.2,492.7490410932 56,492.7490410932 5625456,0.25456 E -12], +--R [6.3,544.5719101259 29,544.5719101259 2903306,0.331 E -13], +--R [6.4,601.8450378720 82,601.8450378720 8205661,0.566 E -13], +--R [6.5,665.1416330443 62,665.1416330443 6184069,- 0.1593 E -12], +--R [6.6,735.0951892419 73,735.0951892419 728949,- 0.1051 E -12], +--R [6.7,812.4058251675 43,812.4058251675 4311346,0.1135 E -12], +--R [6.8,897.8472916504 18,897.8472916504 1769759,- 0.3024 E -12], +--R [6.9,992.2747156050 26,992.2747156050 2587698,- 0.123 E -12], +--R [7.0,1096.6331584284 59,1096.6331584284 585993,- 0.4007 E -12], +--R [7.1,1211.9670744925 77,1211.9670744925 767212,- 0.2788 E -12], +--R [7.2,1339.4307643944 18,1339.4307643944 178297,- 0.1703 E -12], +--R [7.3,1480.2999275845 45,1480.2999275845 452229,0.2228 E -12], +--R [7.4,1635.9844299959 27,1635.9844299959 265401,- 0.4599 E -12], +--R [7.5,1808.0424144560 63,1808.0424144560 632069,0.2069 E -12], +--R [7.6,1998.1958951041 18,1998.1958951041 179592,- 0.408 E -13], +--R [7.7,2208.3479918872 09,2208.3479918872 08524,- 0.476 E -12], +--R [7.8,2440.6019776244 99,2440.6019776244 990773,0.773 E -13], +--R [7.9,2697.2823282685 09,2697.2823282685 088472,- 0.153 E -12], +--R [8.0,2980.9579870417 28,2980.9579870417 282747,0.2747 E -12], +--R [8.1,3294.4680752838 41,3294.4680752838 413332,0.3332 E -12], +--R [8.2,3640.9503073323 55,3640.9503073323 547215,- 0.2785 E -12], +--R [8.3,4023.8723938223 1,4023.8723938223 098416,- 0.158 E -12], +--R [8.4,4447.0667476998 56,4447.0667476998 560855,0.855 E -13], +--R [8.5,4914.7688402991 34,4914.7688402991 343754,0.375 E -12], +--R [8.6,5431.6595913629 8,5431.6595913629 803217,0.322 E -12], +--R [8.7,6002.9122172610 22,6002.9122172610 2198,- 0.2 E -13], +--R [8.8,6634.2440062778 85,6634.2440062778 851586,0.159 E -12], +--R [8.9,7331.9735391559 93,7331.9735391559 929051,- 0.949 E -13], +--R [9.0,8103.0839275753 84,8103.0839275753 840077,0.77 E -14], +--R [9.1,8955.2927034825 12,8955.2927034825 11711,- 0.289 E -12], +--R [9.2,9897.1290587439 16,9897.1290587439 158867,- 0.113 E -12], +--R [9.3,10938.0192081651 84,10938.0192081651 83753,- 0.247 E -12], +--R [9.4,12088.3807302169 84,12088.3807302169 84397,0.397 E -12], +--R [9.5,13359.7268296618 72,13359.7268296618 72276,0.276 E -12], +--R [9.6,14764.7815655772 73,14764.7815655772 72616,- 0.384 E -12], +--R [9.7,16317.6071980154 32,16317.6071980154 32233,0.233 E -12], +--R [9.8,18033.7449278285 11,18033.7449278285 11246,0.246 E -12], +--R [9.9,19930.3704382302 89,19930.3704382302 8949,0.49 E -12], +--R [10.0,22026.4657948067 17,22026.4657948067 16517,- 0.483 E -12]] +--R Type: List List Float +--E 1 + +@ +In the following table there are 4 columns. The first column +is the argument of exp(-x), ranging from 0.0 to 10.0. The +second column is the reference value of exp from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp136-137 + +<<*>>= +--S 2 of 2 +[[0.1,0.90483741803595957316,exp(-0.1),exp(-0.1)-0.90483741803595957316],_ + [0.2,0.81873075307798185867,exp(-0.2),exp(-0.2)-0.81873075307798185867],_ + [0.3,0.74081822068171786607,exp(-0.3),exp(-0.3)-0.74081822068171786607],_ + [0.4,0.67032004603563930074,exp(-0.4),exp(-0.4)-0.67032004603563930074],_ + [0.5,0.60653065971263342360,exp(-0.5),exp(-0.5)-0.60653065971263342360],_ + [0.6,0.54881163609402643263,exp(-0.6),exp(-0.6)-0.54881163609402643263],_ + [0.7,0.49658530379140951470,exp(-0.7),exp(-0.7)-0.49658530379140951470],_ + [0.8,0.44932896411722159143,exp(-0.8),exp(-0.8)-0.44932896411722159143],_ + [0.9,0.40656965974059911188,exp(-0.9),exp(-0.9)-0.40656965974059911188],_ + [1.0,0.36787944117144232160,exp(-1.0),exp(-1.0)-0.36787944117144232160],_ + [1.1,0.33287108369807955329,exp(-1.1),exp(-1.1)-0.33287108369807955329],_ + [1.2,0.30119421191220209664,exp(-1.2),exp(-1.2)-0.30119421191220209664],_ + [1.3,0.27253179303401260312,exp(-1.3),exp(-1.3)-0.27253179303401260312],_ + [1.4,0.24659696394160647694,exp(-1.4),exp(-1.4)-0.24659696394160647694],_ + [1.5,0.22313016014842982893,exp(-1.5),exp(-1.5)-0.22313016014842982893],_ + [1.6,0.20189651799465540849,exp(-1.6),exp(-1.6)-0.20189651799465540849],_ + [1.7,0.18268352405273465022,exp(-1.7),exp(-1.7)-0.18268352405273465022],_ + [1.8,0.16529888822158653830,exp(-1.8),exp(-1.8)-0.16529888822158653830],_ + [1.9,0.14956861922263505264,exp(-1.9),exp(-1.9)-0.14956861922263505264],_ + [2.0,0.13533528323661269189,exp(-2.0),exp(-2.0)-0.13533528323661269189],_ + [2.1,0.12245642825298191022,exp(-2.1),exp(-2.1)-0.12245642825298191022],_ + [2.2,0.11080315836233388333,exp(-2.2),exp(-2.2)-0.11080315836233388333],_ + [2.3,0.10025884372280373373,exp(-2.3),exp(-2.3)-0.10025884372280373373],_ + [2.4,0.09071795328941250338,exp(-2.4),exp(-2.4)-0.09071795328941250338],_ + [2.5,0.08208499862389879517,exp(-2.5),exp(-2.5)-0.08208499862389879517],_ + [2.6,0.07427357821433388043,exp(-2.6),exp(-2.6)-0.07427357821433388043],_ + [2.7,0.06720551273974976513,exp(-2.7),exp(-2.7)-0.06720551273974976513],_ + [2.8,0.06081006262521796500,exp(-2.8),exp(-2.8)-0.06081006262521796500],_ + [2.9,0.05502322005640722903,exp(-2.9),exp(-2.9)-0.05502322005640722903],_ + [3.0,0.04978706836786394298,exp(-3.0),exp(-3.0)-0.04978706836786394298],_ + [3.1,0.04504920239355780607,exp(-3.1),exp(-3.1)-0.04504920239355780607],_ + [3.2,0.04076220397836621517,exp(-3.2),exp(-3.2)-0.04076220397836621517],_ + [3.3,0.03688316740124000545,exp(-3.3),exp(-3.3)-0.03688316740124000545],_ + [3.4,0.03337326996032607948,exp(-3.4),exp(-3.4)-0.03337326996032607948],_ + [3.5,0.03019738342231850074,exp(-3.5),exp(-3.5)-0.03019738342231850074],_ + [3.6,0.02732372244729256080,exp(-3.6),exp(-3.6)-0.02732372244729256080],_ + [3.7,0.02472352647033939120,exp(-3.7),exp(-3.7)-0.02472352647033939120],_ + [3.8,0.02237077185616559578,exp(-3.8),exp(-3.8)-0.02237077185616559578],_ + [3.9,0.02024191144580438847,exp(-3.9),exp(-3.9)-0.02024191144580438847],_ + [4.0,0.01831563888873418029,exp(-4.0),exp(-4.0)-0.01831563888873418029],_ + [4.1,0.01657267540176124754,exp(-4.1),exp(-4.1)-0.01657267540176124754],_ + [4.2,0.01499557682047770621,exp(-4.2),exp(-4.2)-0.01499557682047770621],_ + [4.3,0.01356855901220093176,exp(-4.3),exp(-4.3)-0.01356855901220093176],_ + [4.4,0.01227733990306844118,exp(-4.4),exp(-4.4)-0.01227733990306844118],_ + [4.5,0.01110899653824230650,exp(-4.5),exp(-4.5)-0.01110899653824230650],_ + [4.6,0.01005183574463358164,exp(-4.6),exp(-4.6)-0.01005183574463358164],_ + [4.7,0.00909527710169581709,exp(-4.7),exp(-4.7)-0.00909527710169581709],_ + [4.8,0.00822974704902002884,exp(-4.8),exp(-4.8)-0.00822974704902002884],_ + [4.9,0.00744658307092434052,exp(-4.9),exp(-4.9)-0.00744658307092434052],_ + [5.0,0.00673794699908546710,exp(-5.0),exp(-5.0)-0.00673794699908546710],_ + [5.1,0.00609674656551563611,exp(-5.1),exp(-5.1)-0.00609674656551563611],_ + [5.2,0.00551656442076077242,exp(-5.2),exp(-5.2)-0.00551656442076077242],_ + [5.3,0.00499159390691021621,exp(-5.3),exp(-5.3)-0.00499159390691021621],_ + [5.4,0.00451658094261266798,exp(-5.4),exp(-5.4)-0.00451658094261266798],_ + [5.5,0.00408677143846406699,exp(-5.5),exp(-5.5)-0.00408677143846406699],_ + [5.6,0.00369786371648293082,exp(-5.6),exp(-5.6)-0.00369786371648293082],_ + [5.7,0.00334596545747127277,exp(-5.7),exp(-5.7)-0.00334596545747127277],_ + [5.8,0.00302755474537581475,exp(-5.8),exp(-5.8)-0.00302755474537581475],_ + [5.9,0.00273944481876836923,exp(-5.9),exp(-5.9)-0.00273944481876836923],_ + [6.0,0.00247875217666635842,exp(-6.0),exp(-6.0)-0.00247875217666635842],_ + [6.1,0.00224286771948580247,exp(-6.1),exp(-6.1)-0.00224286771948580247],_ + [6.2,0.00202943063629573436,exp(-6.2),exp(-6.2)-0.00202943063629573436],_ + [6.3,0.00183630477702890683,exp(-6.3),exp(-6.3)-0.00183630477702890683],_ + [6.4,0.00166155727317393450,exp(-6.4),exp(-6.4)-0.00166155727317393450],_ + [6.5,0.00150343919297757245,exp(-6.5),exp(-6.5)-0.00150343919297757245],_ + [6.6,0.00136036803754789342,exp(-6.6),exp(-6.6)-0.00136036803754789342],_ + [6.7,0.00123091190267348118,exp(-6.7),exp(-6.7)-0.00123091190267348118],_ + [6.8,0.00111377514784480308,exp(-6.8),exp(-6.8)-0.00111377514784480308],_ + [6.9,0.00100778542904851076,exp(-6.9),exp(-6.9)-0.00100778542904851076],_ + [7.0,0.00091188196555451621,exp(-7.0),exp(-7.0)-0.00091188196555451621],_ + [7.1,0.00082510492326590427,exp(-7.1),exp(-7.1)-0.00082510492326590427],_ + [7.2,0.00074658580837667937,exp(-7.2),exp(-7.2)-0.00074658580837667937],_ + [7.3,0.00067553877519384424,exp(-7.3),exp(-7.3)-0.00067553877519384424],_ + [7.4,0.00061125276112957256,exp(-7.4),exp(-7.4)-0.00061125276112957256],_ + [7.5,0.00055308437014783358,exp(-7.5),exp(-7.5)-0.00055308437014783358],_ + [7.6,0.00050045143344061070,exp(-7.6),exp(-7.6)-0.00050045143344061070],_ + [7.7,0.00045282718288679706,exp(-7.7),exp(-7.7)-0.00045282718288679706],_ + [7.8,0.00040973497897978671,exp(-7.8),exp(-7.8)-0.00040973497897978671],_ + [7.9,0.00037074354045908837,exp(-7.9),exp(-7.9)-0.00037074354045908837],_ + [8.0,0.00033546262790251184,exp(-8.0),exp(-8.0)-0.00033546262790251184],_ + [8.1,0.00030353913807886666,exp(-8.1),exp(-8.1)-0.00030353913807886666],_ + [8.2,0.00027465356997214233,exp(-8.2),exp(-8.2)-0.00027465356997214233],_ + [8.3,0.00024851682710795202,exp(-8.3),exp(-8.3)-0.00024851682710795202],_ + [8.4,0.00022486732417884827,exp(-8.4),exp(-8.4)-0.00022486732417884827],_ + [8.5,0.00020346836901064417,exp(-8.5),exp(-8.5)-0.00020346836901064417],_ + [8.6,0.00018410579366757912,exp(-8.6),exp(-8.6)-0.00018410579366757912],_ + [8.7,0.00016658581098763341,exp(-8.7),exp(-8.7)-0.00016658581098763341],_ + [8.8,0.00015073307509547660,exp(-8.8),exp(-8.8)-0.00015073307509547660],_ + [8.9,0.00013638892648201145,exp(-8.9),exp(-8.9)-0.00013638892648201145],_ + [9.0,0.00012340980408667955,exp(-9.0),exp(-9.0)-0.00012340980408667955],_ + [9.1,0.00011166580849011474,exp(-9.1),exp(-9.1)-0.00011166580849011474],_ + [9.2,0.00010103940183709335,exp(-9.2),exp(-9.2)-0.00010103940183709335],_ + [9.3,0.00009142423147817334,exp(-9.3),exp(-9.3)-0.00009142423147817334],_ + [9.4,0.00008272406555663226,exp(-9.4),exp(-9.4)-0.00008272406555663226],_ + [9.5,0.00007485182988770059,exp(-9.5),exp(-9.5)-0.00007485182988770059],_ + [9.6,0.00006772873649085387,exp(-9.6),exp(-9.6)-0.00006772873649085387],_ + [9.7,0.00006128349505322210,exp(-9.7),exp(-9.7)-0.00006128349505322210],_ + [9.8,0.00005545159943217698,exp(-9.8),exp(-9.8)-0.00005545159943217698],_ + [9.9,0.00005017468205617530,exp(-9.9),exp(-9.9)-0.00005017468205617530],_ +[10.0,0.00004539992976248485,exp(-10.0),exp(-10.0)-0.00004539992976248485]] +--R +--R +--R (2) +--R [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20], +--R [0.2,0.8187307530 7798185867,0.8187307530 7798185867,0.0], +--R [0.3,0.7408182206 8171786607,0.7408182206 8171786606,- 0.7 E -20], +--R [0.4,0.6703200460 3563930074,0.6703200460 3563930075,0.3 E -20], +--R [0.5,0.6065306597 126334236,0.6065306597 126334236,0.3 E -20], +--R [0.6,0.5488116360 9402643263,0.5488116360 9402643263,- 0.3 E -20], +--R [0.7,0.4965853037 914095147,0.4965853037 9140951471,0.5 E -20], +--R [0.8,0.4493289641 1722159143,0.4493289641 1722159143,0.0], +--R [0.9,0.4065696597 4059911188,0.4065696597 4059911188,0.3 E -20], +--R [1.0,0.3678794411 714423216,0.3678794411 7144232159,- 0.5 E -20], +--R [1.1,0.3328710836 9807955329,0.3328710836 9807955329,- 0.2 E -20], +--R [1.2,0.3011942119 1220209664,0.3011942119 1220209664,0.3 E -20], +--R [1.3,0.2725317930 3401260312,0.2725317930 3401260312,0.3 E -20], +--R [1.4,0.2465969639 4160647694,0.2465969639 4160647694,0.0], +--R [1.5,0.2231301601 4842982893,0.2231301601 4842982893,0.3 E -20], +--R [1.6,0.2018965179 9465540849,0.2018965179 9465540848,- 0.5 E -20], +--R [1.7,0.1826835240 5273465022,0.1826835240 5273465022,0.3 E -20], +--R [1.8,0.1652988882 215865383,0.1652988882 215865383,- 0.3 E -20], +--R [1.9,0.1495686192 2263505264,0.1495686192 2263505264,0.8 E -21], +--R [2.0,0.1353352832 3661269189,0.1353352832 3661269189,0.4 E -20], +--R [2.1,0.1224564282 5298191022,0.1224564282 5298191022,- 0.8 E -21], +--R [2.2,0.1108031583 6233388333,0.1108031583 6233388333,0.4 E -20], +--R [2.3,0.1002588437 2280373373,0.1002588437 2280373373,0.0], +--R [2.4,0.0907179532 8941250338,0.0907179532 8941250337 5,- 0.6 E -20], +--R [2.5,0.0820849986 2389879517,0.0820849986 2389879516 9,- 0.4 E -21], +--R [2.6,0.0742735782 1433388043,0.0742735782 1433388042 9,- 0.1 E -20], +--R [2.7,0.0672055127 3974976513,0.0672055127 3974976512 6,- 0.4 E -20], +--R [2.8,0.0608100626 25217965,0.0608100626 2521796499 6,- 0.4 E -20], +--R [2.9,0.0550232200 5640722903,0.0550232200 5640722903,- 0.4 E -21], +--R [3.0,0.0497870683 6786394298,0.0497870683 6786394297 9,- 0.6 E -21], +--R [3.1,0.0450492023 9355780607,0.0450492023 9355780606 9,- 0.1 E -20], +--R [3.2,0.0407622039 7836621517,0.0407622039 7836621516 6,- 0.4 E -20], +--R [3.3,0.0368831674 0124000545,0.0368831674 0124000544 6,- 0.4 E -20], +--R [3.4,0.0333732699 6032607948,0.0333732699 6032607948 2,0.2 E -20], +--R [3.5,0.0301973834 2231850074,0.0301973834 2231850074,- 0.2 E -21], +--R [3.6,0.0273237224 472925608,0.0273237224 4729256080 2,0.2 E -20], +--R [3.7,0.0247235264 703393912,0.0247235264 7033939120 3,0.3 E -20], +--R [3.8,0.0223707718 5616559578,0.0223707718 5616559577 9,- 0.1 E -20], +--R [3.9,0.0202419114 4580438847,0.0202419114 4580438847 2,0.2 E -20], +--R [4.0,0.0183156388 8873418029,0.0183156388 8873418029 4,0.4 E -20], +--R [4.1,0.0165726754 0176124754,0.0165726754 0176124754 2,0.2 E -20], +--R [4.2,0.0149955768 2047770621,0.0149955768 2047770621 2,0.2 E -20], +--R [4.3,0.0135685590 1220093176,0.0135685590 1220093175 7,- 0.3 E -20], +--R [4.4,0.0122773399 0306844118,0.0122773399 0306844117 9,- 0.1 E -20], +--R [4.5,0.0111089965 382423065,0.0111089965 3824230649 6,- 0.4 E -20], +--R [4.6,0.0100518357 4463358164,0.0100518357 4463358164 2,0.2 E -20], +--R [4.7,0.0090952771 0169581709,0.0090952771 0169581709 21,0.2 E -20], +--R [4.8,0.0082297470 4902002884,0.0082297470 4902002884 13,0.1 E -20], +--R [4.9,0.0074465830 7092434052,0.0074465830 7092434051 82,- 0.2 E -20], +--R [5.0,0.0067379469 990854671,0.0067379469 9908546709 66,- 0.3 E -20], +--R [5.1,0.0060967465 6551563611,0.0060967465 6551563610 72,- 0.3 E -20], +--R [5.2,0.0055165644 2076077242,0.0055165644 2076077241 81,- 0.2 E -20], +--R [5.3,0.0049915939 0691021621,0.0049915939 0691021621 22,0.2 E -20], +--R [5.4,0.0045165809 4261266798,0.0045165809 4261266798 16,0.2 E -20], +--R [5.5,0.0040867714 3846406699,0.0040867714 3846406699 35,0.35 E -20], +--R [5.6,0.0036978637 1648293082,0.0036978637 1648293082 07,0.7 E -21], +--R [5.7,0.0033459654 5747127277,0.0033459654 5747127276 58,- 0.42 E -20], +--R [5.8,0.0030275547 4537581475,0.0030275547 4537581474 82,- 0.18 E -20], +--R [5.9,0.0027394448 1876836923,0.0027394448 1876836923 28,0.28 E -20], +--R [6.0,0.0024787521 7666635842,0.0024787521 7666635842 3,0.3 E -20], +--R [6.1,0.0022428677 1948580247,0.0022428677 1948580247 32,0.32 E -20], +--R [6.2,0.0020294306 3629573436,0.0020294306 3629573436 34,0.34 E -20], +--R [6.3,0.0018363047 7702890683,0.0018363047 7702890682 52,- 0.48 E -20], +--R [6.4,0.0016615572 731739345,0.0016615572 7317393449 91,- 0.93 E -21], +--R [6.5,0.0015034391 9297757245,0.0015034391 9297757244 74,- 0.26 E -20], +--R [6.6,0.0013603680 3754789342,0.0013603680 3754789341 69,- 0.31 E -20], +--R [6.7,0.0012309119 0267348118,0.0012309119 0267348118 46,0.46 E -20], +--R [6.8,0.0011137751 4784480308,0.0011137751 4784480307 88,- 0.12 E -20], +--R [6.9,0.0010077854 2904851076,0.0010077854 2904851076 14,0.14 E -20], +--R [7.0,0.0009118819 6555451621,0.0009118819 6555451620 8,- 0.2 E -20], +--R [7.1,0.0008251049 2326590427,0.0008251049 2326590427 015,0.1 E -21], +--R [7.2,0.0007465858 0837667937,0.0007465858 0837667936 81,- 0.19 E -20], +--R [7.3,0.0006755387 7519384424,0.0006755387 7519384423 783,- 0.22 E -20], +--R [7.4,0.0006112527 6112957256,0.0006112527 6112957255 567,- 0.433 E -20], +--R [7.5,0.0005530843 7014783358,0.0005530843 7014783358 31,0.31 E -20], +--R [7.6,0.0005004514 334406107,0.0005004514 3344061069 551,- 0.449 E -20], +--R [7.7,0.0004528271 8288679706,0.0004528271 8288679705 8,- 0.2 E -20], +--R [7.8,0.0004097349 7897978671,0.0004097349 7897978670 846,- 0.15 E -20], +--R [7.9,0.0003707435 4045908837,0.0003707435 4045908837 443,0.443 E -20], +--R [8.0,0.0003354626 2790251184,0.0003354626 2790251183 882,- 0.12 E -20], +--R [8.1,0.0003035391 3807886666,0.0003035391 3807886666 086,0.86 E -21], +--R [8.2,0.0002746535 6997214233,0.0002746535 6997214232 763,- 0.237 E -20], +--R [8.3,0.0002485168 2710795202,0.0002485168 2710795202 08,0.8 E -21], +--R [8.4,0.0002248673 2417884827,0.0002248673 2417884827 28,0.28 E -20], +--R [8.5,0.0002034683 6901064417,0.0002034683 6901064417 437,0.437 E -20], +--R [8.6,0.0001841057 9366757912,0.0001841057 9366757912 495,0.495 E -20], +--R [8.7,0.0001665858 1098763341,0.0001665858 1098763341 149,0.149 E -20], +--R [8.8,0.0001507330 750954766,0.0001507330 7509547660 064,0.64 E -21], +--R [8.9,0.0001363889 2648201145,0.0001363889 2648201144 785,- 0.215 E -20], +--R [9.0,0.0001234098 0408667955,0.0001234098 0408667954 95,- 0.5 E -21], +--R [9.1,0.0001116658 0849011474,0.0001116658 0849011473 564,- 0.436 E -20], +--R [9.2,0.0001010394 0183709335,0.0001010394 0183709335 073,0.732 E -21], +--R [9.3,0.0000914242 3147817334,0.0000914242 3147817333 7862,- 0.214 E -20], +--R [9.4,0.0000827240 6555663226,0.0000827240 6555663226 2731,0.273 E -20], +--R [9.5,0.0000748518 2988770059,0.0000748518 2988770059 1471,0.147 E -20], +--R [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20], +--R [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20], +--R [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20], +--R [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20], +--R [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp136-137 +\end{thebibliography} +\end{document} + diff --git a/src/input/gamma.input.pamphlet b/src/input/gamma.input.pamphlet index 608cf75..6b5f38b 100644 --- a/src/input/gamma.input.pamphlet +++ b/src/input/gamma.input.pamphlet @@ -17,19 +17,13 @@ second column is the reference value of Gamma from the book Abramowitz and Stegun, ``Handbook of Mathematical Functions'', Dover Publications, Inc. New York 1965. pp267-270 -Notice that certain entries have reasonably large differences: -\begin{verbatim} -[1.215, 0.9143261399876792, 0.91432614997006778, 9.9823885824079639E-9] -[1.455, 0.88562206999631599, 0.88562207999314335, 9.9968273659101214E-9] -\end{verbatim} - <<*>>= )spool gamma.output )set message test on )set message auto off )clear all ---S 1 of 3 +--S 1 of 4 [[1.000,1.0000000000,Gamma(1.000),Gamma(1.000)-1.0000000000],_ [1.005,0.9971385354,Gamma(1.005),Gamma(1.005)-0.9971385354],_ [1.010,0.9943258512,Gamma(1.010),Gamma(1.010)-0.9943258512],_ @@ -73,7 +67,7 @@ Notice that certain entries have reasonably large differences: [1.200,0.9181687424,Gamma(1.200),Gamma(1.200)-0.9181687424],_ [1.205,0.9168572606,Gamma(1.205),Gamma(1.205)-0.9168572606],_ [1.210,0.9155764930,Gamma(1.210),Gamma(1.210)-0.9155764930],_ - [1.215,0.9143261400,Gamma(1.215),Gamma(1.215)-0.9143261400],_ + [1.215,0.9143261500,Gamma(1.215),Gamma(1.215)-0.9143261500],_ [1.220,0.9131059475,Gamma(1.220),Gamma(1.220)-0.9131059475],_ [1.225,0.9119156071,Gamma(1.225),Gamma(1.225)-0.9119156071],_ [1.230,0.9107548564,Gamma(1.230),Gamma(1.230)-0.9107548564],_ @@ -121,7 +115,7 @@ Notice that certain entries have reasonably large differences: [1.440,0.8858050635,Gamma(1.440),Gamma(1.440)-0.8858050635],_ [1.445,0.8857223397,Gamma(1.445),Gamma(1.445)-0.8857223397],_ [1.450,0.8856613803,Gamma(1.450),Gamma(1.450)-0.8856613803],_ - [1.455,0.8856220700,Gamma(1.455),Gamma(1.455)-0.8856220700],_ + [1.455,0.8856220800,Gamma(1.455),Gamma(1.455)-0.8856220800],_ [1.460,0.8856043364,Gamma(1.460),Gamma(1.460)-0.8856043364],_ [1.465,0.8856080495,Gamma(1.465),Gamma(1.465)-0.8856080495],_ [1.470,0.8856331217,Gamma(1.470),Gamma(1.470)-0.8856331217],_ @@ -349,8 +343,8 @@ Notice that certain entries have reasonably large differences: --R , --R [1.21,0.91557649299999999,0.91557649300335908,3.3590907833058736E-12], --R ---R [1.2150000000000001, 0.91432614000000001, 0.91432614997639472, ---R 9.9763947103426176E-9] +--R [1.2150000000000001, 0.91432614999999995, 0.91432614997639472, +--R - 2.3605228882672691E-11] --R , --R [1.22,0.91310594749999996,0.9131059475104113,1.041133845802733E-11], --R @@ -475,8 +469,8 @@ Notice that certain entries have reasonably large differences: --R , --R [1.45,0.88566138029999997,0.88566138027107244,- 2.8927527040423229E-11], --R ---R [1.4550000000000001, 0.88562207000000004, 0.88562207999323628, ---R 9.9932362385146689E-9] +--R [1.4550000000000001, 0.88562207999999998, 0.88562207999323628, +--R - 6.7637007106213787E-12] --R , --R [1.46,0.88560433640000003,0.88560433642514391,2.5143886972500695E-11], --R @@ -762,7 +756,7 @@ Notice that certain entries have reasonably large differences: --R Type: List List DoubleFloat --E 1 ---S 2 of 3 +--S 2 of 4 Psi(x:DFLOAT):DFLOAT==polygamma(0,x) --R --R Function declaration Psi : DoubleFloat -> DoubleFloat has been added @@ -778,7 +772,7 @@ Dover Publications, Inc. New York 1965. pp267-270 <<*>>= ---S 3 of 3 +--S 3 of 4 [[1.000, -0.5772156649, Psi(1.000), Psi(1.000)- -0.5772156649],_ [1.005, -0.5690209113, Psi(1.005), Psi(1.005)- -0.5690209113],_ [1.010, -0.5608854579, Psi(1.010), Psi(1.010)- -0.5608854579],_ @@ -1540,6 +1534,836 @@ Dover Publications, Inc. New York 1965. pp267-270 --R [2.,0.42278433510000002,0.42278433509846725,- 1.5327739077974911E-12]] --R Type: List List DoubleFloat --E 3 +@ +In the following table there are 4 columns. The first column +is the argument of complex Gamma, ranging from 1.0 + 0i to 1.0+10i +second column is the reference value of complex Gamma from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp227 + +Note that at the value 1.0+4.6i there is a radical departure between +the table and the computed values in the imaginary part of the value +even though the real part is exact. +<<*>>= +--S 4 of 4 +[[1. + 0.0 * %i,0.,log(Gamma(1. + 0.0 * %i)),log(Gamma(1. + 0.0 * %i))-0.0],_ +[1. + 0.1 * %i, -0.008197780565 - 0.057322940417 * %i,_ +log(Gamma(1. + 0.1 * %i)),_ +log(Gamma(1. + 0.1 * %i))-( -0.008197780565 - 0.057322940417 * %i)],_ +[1. + 0.2 * %i, -0.032476292318 - 0.112302222644 * %i,_ +log(Gamma(1. + 0.2 * %i)),_ +log(Gamma(1. + 0.2 * %i))-( -0.032476292318 - 0.112302222644 * %i)],_ +[1. + 0.3 * %i, -0.071946250900 - 0.162820672168 * %i,_ +log(Gamma(1. + 0.3 * %i)),_ +log(Gamma(1. + 0.3 * %i))-( -0.071946250900 - 0.162820672168 * %i)],_ +[1. + 0.4 * %i, -0.125289374821 - 0.207155826316 * %i,_ +log(Gamma(1. + 0.4 * %i)),_ +log(Gamma(1. + 0.4 * %i))-( -0.125289374821 - 0.207155826316 * %i)],_ +[1. + 0.5 * %i,- 0.190945499187 - 0.244058298905 * %i,_ +log(Gamma(1. + 0.5 * %i)),_ +log(Gamma(1. + 0.5 * %i))-(- 0.190945499187 - 0.244058298905 * %i)],_ +[1. + 0.6 * %i,- 0.267290068214 - 0.272743810491 * %i,_ +log(Gamma(1. + 0.6 * %i)),_ +log(Gamma(1. + 0.6 * %i))-(- 0.267290068214 - 0.272743810491 * %i)],_ +[1. + 0.7 * %i,- 0.352768690860 - 0.292826351187 * %i,_ +log(Gamma(1. + 0.7 * %i)),_ +log(Gamma(1. + 0.7 * %i))-(- 0.352768690860 - 0.292826351187 * %i)],_ +[1. + 0.8 * %i,- 0.445978783549 - 0.304225602976 * %i,_ +log(Gamma(1. + 0.8 * %i)),_ +log(Gamma(1. + 0.8 * %i))-(- 0.445978783549 - 0.304225602976 * %i)],_ +[1. + 0.9 * %i,- 0.545705128605 - 0.307074375642 * %i,_ +log(Gamma(1. + 0.9 * %i)),_ +log(Gamma(1. + 0.9 * %i))-(- 0.545705128605 - 0.307074375642 * %i)],_ +[1. + 1.0 * %i,- 0.650923199302 - 0.301640320468 * %i,_ +log(Gamma(1. + 1.0 * %i)),_ +log(Gamma(1. + 1.0 * %i))-(- 0.650923199302 - 0.301640320468 * %i)],_ +[1. + 1.1 * %i,- 0.760783958841 - 0.288266614239 * %i,_ +log(Gamma(1. + 1.1 * %i)),_ +log(Gamma(1. + 1.1 * %i))-(- 0.760783958841 - 0.288266614239 * %i)],_ +[1. + 1.2 * %i,- 0.874590463895 - 0.267330580581 * %i,_ +log(Gamma(1. + 1.2 * %i)),_ +log(Gamma(1. + 1.2 * %i))-(- 0.874590463895 - 0.267330580581 * %i)],_ +[1. + 1.3 * %i,- 0.991772766959 - 0.239216784465 * %i,_ +log(Gamma(1. + 1.3 * %i)),_ +log(Gamma(1. + 1.3 * %i))-(- 0.991772766959 - 0.239216784465 * %i)],_ +[1. + 1.4 * %i,- 1.111864566426 - 0.204300724149 * %i,_ +log(Gamma(1. + 1.4 * %i)),_ +log(Gamma(1. + 1.4 * %i))-(- 1.111864566426 - 0.204300724149 * %i)],_ +[1. + 1.5 * %i,- 1.234483051547 - 0.162939769480 * %i,_ +log(Gamma(1. + 1.5 * %i)),_ +log(Gamma(1. + 1.5 * %i))-(- 1.234483051547 - 0.162939769480 * %i)],_ +[1. + 1.6 * %i,- 1.359312248465 - 0.115468793589 * %i,_ +log(Gamma(1. + 1.6 * %i)),_ +log(Gamma(1. + 1.6 * %i))-(- 1.359312248465 - 0.115468793589 * %i)],_ +[1. + 1.7 * %i,- 1.486089612757 - 0.062198698329 * %i,_ +log(Gamma(1. + 1.7 * %i)),_ +log(Gamma(1. + 1.7 * %i))-(- 1.486089612757 - 0.062198698329 * %i)],_ +[1. + 1.8 * %i,- 1.614595396000 - 0.003416631477 * %i,_ +log(Gamma(1. + 1.8 * %i)),_ +log(Gamma(1. + 1.8 * %i))-(- 1.614595396000 - 0.003416631477 * %i)],_ +[1. + 1.9 * %i,- 1.744644276174 + 0.060612874295 * %i,_ +log(Gamma(1. + 1.9 * %i)),_ +log(Gamma(1. + 1.9 * %i))-(- 1.744644276174 + 0.060612874295 * %i)],_ +[1. + 2.0 * %i,- 1.876078786431 + 0.129646316310 * %i,_ +log(Gamma(1. + 2.0 * %i)),_ +log(Gamma(1. + 2.0 * %i))-(- 1.876078786431 + 0.129646316310 * %i)],_ +[1. + 2.1 * %i,- 2.008764150471 + 0.203459473833 * %i,_ +log(Gamma(1. + 2.1 * %i)),_ +log(Gamma(1. + 2.1 * %i))-(- 2.008764150471 + 0.203459473833 * %i)],_ +[1. + 2.2 * %i,- 2.142584209296 + 0.281845658426 * %i,_ +log(Gamma(1. + 2.2 * %i)),_ +log(Gamma(1. + 2.2 * %i))-(- 2.142584209296 + 0.281845658426 * %i)],_ +[1. + 2.3 * %i,- 2.277438192204 + 0.364614048950 * %i,_ +log(Gamma(1. + 2.3 * %i)),_ +log(Gamma(1. + 2.3 * %i))-(- 2.277438192204 + 0.364614048950 * %i)],_ +[1. + 2.4 * %i,- 2.413238141184 + 0.451588152441 * %i,_ +log(Gamma(1. + 2.4 * %i)),_ +log(Gamma(1. + 2.4 * %i))-(- 2.413238141184 + 0.451588152441 * %i)],_ +[1. + 2.5 * %i,- 2.549906842495 + 0.542604405852 * %i,_ +log(Gamma(1. + 2.5 * %i)),_ +log(Gamma(1. + 2.5 * %i))-(- 2.549906842495 + 0.542604405852 * %i)],_ +[1. + 2.6 * %i,- 2.687376153750 + 0.637510919046 * %i,_ +log(Gamma(1. + 2.6 * %i)),_ +log(Gamma(1. + 2.6 * %i))-(- 2.687376153750 + 0.637510919046 * %i)],_ +[1. + 2.7 * %i,- 2.825585641191 + 0.736166351679 * %i,_ +log(Gamma(1. + 2.7 * %i)),_ +log(Gamma(1. + 2.7 * %i))-(- 2.825585641191 + 0.736166351679 * %i)],_ +[1. + 2.8 * %i,- 2.964481461789 + 0.838438913096 * %i,_ +log(Gamma(1. + 2.8 * %i)),_ +log(Gamma(1. + 2.8 * %i))-(- 2.964481461789 + 0.838438913096 * %i)],_ +[1. + 2.9 * %i,- 3.104015439901 + 0.944205473039 * %i,_ +log(Gamma(1. + 2.9 * %i)),_ +log(Gamma(1. + 2.9 * %i))-(- 3.104015439901 + 0.944205473039 * %i)],_ +[1. + 3.0 * %i,- 3.244144299590 + 1.053350771069 * %i,_ +log(Gamma(1. + 3.0 * %i)),_ +log(Gamma(1. + 3.0 * %i))-(- 3.244144299590 + 1.053350771069 * %i)],_ +[1. + 3.1 * %i,- 3.384829022377 + 1.165766713286 * %i,_ +log(Gamma(1. + 3.1 * %i)),_ +log(Gamma(1. + 3.1 * %i))-(- 3.384829022377 + 1.165766713286 * %i)],_ +[1. + 3.2 * %i,- 3.526034306709 + 1.281351745932 * %i,_ +log(Gamma(1. + 3.2 * %i)),_ +log(Gamma(1. + 3.2 * %i))-(- 3.526034306709 + 1.281351745932 * %i)],_ +[1. + 3.3 * %i,- 3.667728110488 + 1.400010296576 * %i,_ +log(Gamma(1. + 3.3 * %i)),_ +log(Gamma(1. + 3.3 * %i))-(- 3.667728110488 + 1.400010296576 * %i)],_ +[1. + 3.4 * %i,- 3.809881261823 + 1.521652274673 * %i,_ +log(Gamma(1. + 3.4 * %i)),_ +log(Gamma(1. + 3.4 * %i))-(- 3.809881261823 + 1.521652274673 * %i)],_ +[1. + 3.5 * %i,- 3.952467126189 + 1.646192624269 * %i,_ +log(Gamma(1. + 3.5 * %i)),_ +log(Gamma(1. + 3.5 * %i))-(- 3.952467126189 + 1.646192624269 * %i)],_ +[1. + 3.6 * %i,- 4.095461320451 + 1.773550922591 * %i,_ +log(Gamma(1. + 3.6 * %i)),_ +log(Gamma(1. + 3.6 * %i))-(- 4.095461320451 + 1.773550922591 * %i)],_ +[1. + 3.7 * %i,- 4.238841466071 + 1.903651019019 * %i,_ +log(Gamma(1. + 3.7 * %i)),_ +log(Gamma(1. + 3.7 * %i))-(- 4.238841466071 + 1.903651019019 * %i)],_ +[1. + 3.8 * %i,- 4.382586975228 + 2.036420709693 * %i,_ +log(Gamma(1. + 3.8 * %i)),_ +log(Gamma(1. + 3.8 * %i))-(- 4.382586975228 + 2.036420709693 * %i)],_ +[1. + 3.9 * %i,- 4.526678864716 + 2.171791443605 * %i,_ +log(Gamma(1. + 3.9 * %i)),_ +log(Gamma(1. + 3.9 * %i))-(- 4.526678864716 + 2.171791443605 * %i)],_ +[1. + 4.0 * %i,- 4.671099593409 + 2.309698056573 * %i,_ +log(Gamma(1. + 4.0 * %i)),_ +log(Gamma(1. + 4.0 * %i))-(- 4.671099593409 + 2.309698056573 * %i)],_ +[1. + 4.1 * %i,- 4.815832919796 + 2.450078529947 * %i,_ +log(Gamma(1. + 4.1 * %i)),_ +log(Gamma(1. + 4.1 * %i))-(- 4.815832919796 + 2.450078529947 * %i)],_ +[1. + 4.2 * %i,- 4.960863776687 + 2.592873771319 * %i,_ +log(Gamma(1. + 4.2 * %i)),_ +log(Gamma(1. + 4.2 * %i))-(- 4.960863776687 + 2.592873771319 * %i)],_ +[1. + 4.3 * %i,- 5.106178160663 + 2.738027414820 * %i,_ +log(Gamma(1. + 4.3 * %i)),_ +log(Gamma(1. + 4.3 * %i))-(- 5.106178160663 + 2.738027414820 * %i)],_ +[1. + 4.4 * %i,- 5.251763034230 + 2.885485638927 * %i,_ +log(Gamma(1. + 4.4 * %i)),_ +log(Gamma(1. + 4.4 * %i))-(- 5.251763034230 + 2.885485638927 * %i)],_ +[1. + 4.5 * %i,- 5.397606238984 + 3.035196999922 * %i,_ +log(Gamma(1. + 4.5 * %i)),_ +log(Gamma(1. + 4.5 * %i))-(- 5.397606238984 + 3.035196999922 * %i)],_ +[1. + 4.6 * %i,- 5.543696418304 + 3.187112279389 * %i,_ +log(Gamma(1. + 4.6 * %i)),_ +log(Gamma(1. + 4.6 * %i))-(- 5.543696418304 + 3.187112279389 * %i)],_ +[1. + 4.7 * %i,- 5.690022948373 + 3.341184344327 * %i,_ +log(Gamma(1. + 4.7 * %i)),_ +log(Gamma(1. + 4.7 * %i))-(- 5.690022948373 + 3.341184344327 * %i)],_ +[1. + 4.8 * %i,- 5.836575876454 + 3.497368018615 * %i,_ +log(Gamma(1. + 4.8 * %i)),_ +log(Gamma(1. + 4.8 * %i))-(- 5.836575876454 + 3.497368018615 * %i)],_ +[1. + 4.9 * %i,- 5.983345865532 + 3.655619964712 * %i,_ +log(Gamma(1. + 4.9 * %i)),_ +log(Gamma(1. + 4.9 * %i))-(- 5.983345865532 + 3.655619964712 * %i)],_ +[1. + 5.0 * %i,- 6.130324144553 + 3.815898574615 * %i,_ +log(Gamma(1. + 5.0 * %i)),_ +log(Gamma(1. + 5.0 * %i))-(- 6.130324144553 + 3.815898574615 * %i)],_ +[1. + 5.1 * %i,- 6.277502463584 + 3.978163869188 * %i,_ +log(Gamma(1. + 5.1 * %i)),_ +log(Gamma(1. + 5.1 * %i))-(- 6.277502463584 + 3.978163869188 * %i)],_ +[1. + 5.2 * %i,- 6.424873053335 + 4.142377405086 * %i,_ +log(Gamma(1. + 5.2 * %i)),_ +log(Gamma(1. + 5.2 * %i))-(- 6.424873053335 + 4.142377405086 * %i)],_ +[1. + 5.3 * %i,- 6.572428588529 + 4.308502188583 * %i,_ +log(Gamma(1. + 5.3 * %i)),_ +log(Gamma(1. + 5.3 * %i))-(- 6.572428588529 + 4.308502188583 * %i)],_ +[1. + 5.4 * %i,- 6.720162154703 + 4.476502595668 * %i,_ +log(Gamma(1. + 5.4 * %i)),_ +log(Gamma(1. + 5.4 * %i))-(- 6.720162154703 + 4.476502595668 * %i)],_ +[1. + 5.5 * %i,- 6.868067218048 + 4.646344297870 * %i,_ +log(Gamma(1. + 5.5 * %i)),_ +log(Gamma(1. + 5.5 * %i))-(- 6.868067218048 + 4.646344297870 * %i)],_ +[1. + 5.6 * %i,- 7.016137597976 + 4.817994193305 * %i,_ +log(Gamma(1. + 5.6 * %i)),_ +log(Gamma(1. + 5.6 * %i))-(- 7.016137597976 + 4.817994193305 * %i)],_ +[1. + 5.7 * %i,- 7.164367442106 + 4.991420342489 * %i,_ +log(Gamma(1. + 5.7 * %i)),_ +log(Gamma(1. + 5.7 * %i))-(- 7.164367442106 + 4.991420342489 * %i)],_ +[1. + 5.8 * %i,- 7.312751203430 + 5.166591908537 * %i,_ +log(Gamma(1. + 5.8 * %i)),_ +log(Gamma(1. + 5.8 * %i))-(- 7.312751203430 + 5.166591908537 * %i)],_ +[1. + 5.9 * %i,- 7.461283619429 + 5.343479101353 * %i,_ +log(Gamma(1. + 5.9 * %i)),_ +log(Gamma(1. + 5.9 * %i))-(- 7.461283619429 + 5.343479101353 * %i)],_ +[1. + 6.0 * %i,- 7.609959692951 + 5.522053125515 * %i,_ +log(Gamma(1. + 6.0 * %i)),_ +log(Gamma(1. + 6.0 * %i))-(- 7.609959692951 + 5.522053125515 * %i)],_ +[1. + 6.1 * %i,- 7.758774674655 + 5.702286131535 * %i,_ +log(Gamma(1. + 6.1 * %i)),_ +log(Gamma(1. + 6.1 * %i))-(- 7.758774674655 + 5.702286131535 * %i)],_ +[1. + 6.2 * %i,- 7.907724046898 + 5.884151170239 * %i,_ +log(Gamma(1. + 6.2 * %i)),_ +log(Gamma(1. + 6.2 * %i))-(- 7.907724046898 + 5.884151170239 * %i)],_ +[1. + 6.3 * %i,- 8.056803508904 + 6.067622150013 * %i,_ +log(Gamma(1. + 6.3 * %i)),_ +log(Gamma(1. + 6.3 * %i))-(- 8.056803508904 + 6.067622150013 * %i)],_ +[1. + 6.4 * %i,- 8.206008963100 + 6.252673796705 * %i,_ +log(Gamma(1. + 6.4 * %i)),_ +log(Gamma(1. + 6.4 * %i))-(- 8.206008963100 + 6.252673796705 * %i)],_ +[1. + 6.5 * %i,- 8.355336502511 + 6.439281615976 * %i,_ +log(Gamma(1. + 6.5 * %i)),_ +log(Gamma(1. + 6.5 * %i))-(- 8.355336502511 + 6.439281615976 * %i)],_ +[1. + 6.6 * %i,- 8.504782399125 + 6.627421857912 * %i,_ +log(Gamma(1. + 6.6 * %i)),_ +log(Gamma(1. + 6.6 * %i))-(- 8.504782399125 + 6.627421857912 * %i)],_ +[1. + 6.7 * %i,- 8.654343093123 + 6.817071483744 * %i,_ +log(Gamma(1. + 6.7 * %i)),_ +log(Gamma(1. + 6.7 * %i))-(- 8.654343093123 + 6.817071483744 * %i)],_ +[1. + 6.8 * %i,- 8.804015182910 + 7.008208134502 * %i,_ +log(Gamma(1. + 6.8 * %i)),_ +log(Gamma(1. + 6.8 * %i))-(- 8.804015182910 + 7.008208134502 * %i)],_ +[1. + 6.9 * %i,- 8.953795415879 + 7.200810101493 * %i,_ +log(Gamma(1. + 6.9 * %i)),_ +log(Gamma(1. + 6.9 * %i))-(- 8.953795415879 + 7.200810101493 * %i)],_ +[1. + 7.0 * %i,- 9.103680679832 + 7.394856298436 * %i,_ +log(Gamma(1. + 7.0 * %i)),_ +log(Gamma(1. + 7.0 * %i))-(- 9.103680679832 + 7.394856298436 * %i)],_ +[1. + 7.1 * %i,- 9.253667995015 + 7.590326235184 * %i,_ +log(Gamma(1. + 7.1 * %i)),_ +log(Gamma(1. + 7.1 * %i))-(- 9.253667995015 + 7.590326235184 * %i)],_ +[1. + 7.2 * %i,- 9.403754506708 + 7.787199992877 * %i,_ +log(Gamma(1. + 7.2 * %i)),_ +log(Gamma(1. + 7.2 * %i))-(- 9.403754506708 + 7.787199992877 * %i)],_ +[1. + 7.3 * %i,- 9.553937478321 + 7.985458200468 * %i,_ +log(Gamma(1. + 7.3 * %i)),_ +log(Gamma(1. + 7.3 * %i))-(- 9.553937478321 + 7.985458200468 * %i)],_ +[1. + 7.4 * %i,- 9.704214284972 + 8.185082012503 * %i,_ +log(Gamma(1. + 7.4 * %i)),_ +log(Gamma(1. + 7.4 * %i))-(- 9.704214284972 + 8.185082012503 * %i)],_ +[1. + 7.5 * %i,- 9.854582407486 + 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4.4408920985006262E-14 - 6.2831853071792185 %i] +--R , +--R +--R [1. + 5.5999999999999996 %i, - 7.0161375979759999 + 4.8179941933050001 %i, +--R - 7.0161375979761953 - 1.4651911138747613 %i, +--R - 1.9539925233402755E-13 - 6.2831853071797612 %i] +--R , +--R +--R [1. + 5.7000000000000002 %i, - 7.1643674421060002 + 4.9914203424889996 %i, +--R - 7.1643674421059877 - 1.2917649646901792 %i, +--R 1.2434497875801753E-14 - 6.2831853071791786 %i] +--R , +--R +--R [1. + 5.7999999999999998 %i, - 7.3127512034300004 + 5.1665919085369998 %i, +--R - 7.3127512034295403 - 1.1165933986428442 %i, +--R 4.6007642140466487E-13 - 6.2831853071798438 %i] +--R , +--R +--R [1. + 5.9000000000000004 %i, - 7.4612836194290004 + 5.3434791013530001 %i, +--R - 7.4612836194293823 - 0.93970620582698861 %i, +--R - 3.8191672047105385E-13 - 6.2831853071799886 %i] +--R , +--R +--R [1. + 6. %i, - 7.6099596929509996 + 5.5220531255149998 %i, +--R - 7.6099596929506781 - 0.76113218166486107 %i, +--R 3.2152058793144533E-13 - 6.2831853071798607 %i] +--R , +--R +--R [1. + 6.0999999999999996 %i, - 7.7587746746550001 + 5.7022861315349997 %i, +--R - 7.7587746746545623 - 0.58089917564415772 %i, +--R 4.3787196091216174E-13 - 6.2831853071791572 %i] +--R , +--R +--R [1. + 6.2000000000000002 %i, - 7.9077240468980001 + 5.8841511702389999 %i, +--R - 7.9077240468981636 - 0.39903413694019135 %i, +--R - 1.6342482922482304E-13 - 6.283185307179191 %i] +--R , +--R +--R [1. + 6.2999999999999998 %i, - 8.0568035089040002 + 6.0676221500130003 %i, +--R - 8.0568035089044336 - 0.21556315716640231 %i, +--R - 4.3343106881366111E-13 - 6.2831853071794024 %i] +--R , +--R +--R [1. + 6.4000000000000004 %i, - 8.2060089631000004 + 6.2526737967050003 %i, +--R - 8.2060089630998547 - 3.0511510474225532E-2 %i, +--R 1.4566126083082054E-13 - 6.2831853071792256 %i] +--R , +--R +--R [1. + 6.5 %i, - 8.3553365025109994 + 6.4392816159760002 %i, +--R - 8.3553365025113582 + 0.15609630879639777 %i, +--R - 3.5882408155885059E-13 - 6.2831853071796022 %i] +--R , +--R +--R [1. + 6.5999999999999996 %i, - 8.5047823991250002 + 6.6274218579120001 %i, +--R - 8.5047823991254532 + 0.34423655073274489 %i, +--R - 4.5297099404706387E-13 - 6.2831853071792549 %i] +--R , +--R +--R [1. + 6.7000000000000002 %i, - 8.6543430931229999 + 6.8170714837439998 %i, +--R - 8.654343093122673 + 0.53388617656407311 %i, +--R 3.2684965844964609E-13 - 6.2831853071799264 %i] +--R , +--R +--R [1. + 6.7999999999999998 %i, - 8.8040151829099997 + 7.0082081345020004 %i, +--R - 8.804015182909593 + 0.72502282732285273 %i, +--R 4.0678571622265736E-13 - 6.2831853071791475 %i] +--R , +--R +--R [1. + 6.9000000000000004 %i, - 8.9537954158790001 + 7.2008101014930004 %i, +--R - 8.9537954158785062 + 0.91762479431292798 %i, +--R 4.9382720135326963E-13 - 6.2831853071800721 %i] +--R , +--R +--R [1. + 7. %i, - 9.1036806798319994 + 7.3948562984360002 %i, +--R - 9.1036806798319478 + 1.1116709912566856 %i, +--R 5.1514348342607263E-14 - 6.2831853071793144 %i] +--R , +--R +--R [1. + 7.0999999999999996 %i, - 9.2536679950150003 + 7.5903262351840004 %i, +--R - 9.2536679950154568 + 1.3071409280042976 %i, +--R - 4.5652370772586437E-13 - 6.2831853071797026 %i] +--R , +--R +--R [1. + 7.2000000000000002 %i, - 9.4037545067079993 + 7.7871999928770004 %i, +--R - 9.4037545067075801 + 1.5040146856973393 %i, +--R 4.1922021409845911E-13 - 6.2831853071796608 %i] +--R , +--R +--R [1. + 7.2999999999999998 %i, - 9.553937478321 + 7.9854582004679999 %i, +--R - 9.5539374783209006 + 1.7022728932880065 %i, +--R 9.9475983006414026E-14 - 6.283185307179993 %i] +--R , +--R +--R [1. + 7.4000000000000004 %i, - 9.7042142849720001 + 8.1850820125030008 %i, +--R - 9.7042142849724993 + 1.9018967053232116 %i, +--R - 4.9915627187147038E-13 - 6.2831853071797887 %i] +--R , +--R +--R [1. + 7.5 %i, - 9.8545824074859993 + 8.3860530880889996 %i, +--R - 9.8545824074859194 + 2.1028677809095977 %i, +--R 7.9936057773011271E-14 - 6.2831853071794015 %i] +--R , +--R +--R [1. + 7.5999999999999996 %i, - 10.005039426790001 + 8.5883535709619991 %i, +--R - 10.005039426790399 + 2.3051682637825208 %i, +--R - 3.979039320256561E-13 - 6.2831853071794779 %i] +--R , +--R +--R [1. + 7.7000000000000002 %i, - 10.155583018686 + 8.7919660705869997 %i, +--R - 10.155583018686212 + 2.5087807634076618 %i, +--R - 2.1138646388862981E-13 - 6.2831853071793375 %i] +--R , +--R +--R [1. + 7.7999999999999998 %i, - 10.306210948947999 + 8.9968736442289998 %i, +--R - 10.306210948947749 + 2.7136883370494931 %i, +--R 2.5046631435543532E-13 - 6.2831853071795063 %i] +--R , +--R +--R [1. + 7.9000000000000004 %i, - 10.456921068739 + 9.2030597799250007 %i, +--R - 10.456921068738524 + 2.9198744727458439 %i, +--R 4.7606363295926712E-13 - 6.2831853071791564 %i] +--R , +--R +--R [1. + 8. %i, - 10.607711310315 + 9.4105083803120007 %i, +--R - 10.607711310314581 + 3.1273230731320214 %i, +--R 4.1922021409845911E-13 - 6.2831853071799788 %i] +--R , +--R +--R [1. + 8.0999999999999996 %i, - 10.758579682995 + 9.6192037472420004 %i, +--R - 10.758579682994794 - 2.9471668671170055 %i, +--R 2.0605739337042905E-13 - 12.566370614359005 %i] +--R , +--R +--R [1. + 8.1999999999999993 %i, - 10.909524269378 + 9.8291305671620002 %i, +--R - 10.909524269378375 - 2.7372400471974712 %i, +--R - 3.7481129311345285E-13 - 12.566370614359471 %i] +--R , +--R +--R [1. + 8.3000000000000007 %i, - 11.060543221792001 + 10.040273897180001 %i, +--R - 11.060543221791693 - 2.5260967171793411 %i, +--R 3.0730973321624333E-13 - 12.566370614359341 %i] +--R , +--R +--R [1. + 8.4000000000000004 %i, - 11.211634758948 + 10.252619151809 %i, +--R - 11.211634758947826 - 2.3137514625505582 %i, +--R 1.7408297026122455E-13 - 12.566370614359558 %i] +--R , +--R +--R [1. + 8.5 %i, - 11.362797162804 + 10.466152090324 %i, +--R - 11.362797162803814 - 2.100218524035578 %i, +--R 1.865174681370263E-13 - 12.566370614359577 %i] +--R , +--R +--R [1. + 8.5999999999999996 %i, - 11.514028775602 + 10.680858804712001 %i, +--R - 11.514028775601707 - 1.8855118096468773 %i, +--R 2.9309887850104133E-13 - 12.566370614358878 %i] +--R , +--R +--R [1. + 8.6999999999999993 %i, - 11.665327997081 + 10.896725708177 %i, +--R - 11.665327997080658 - 1.6696449061826013 %i, +--R 3.4283687000424834E-13 - 12.566370614359601 %i] +--R , +--R +--R [1. + 8.8000000000000007 %i, - 11.816693281848 + 11.113739524156999 %i, +--R - 11.816693281848337 - 1.452631090201765 %i, +--R - 3.3750779948604759E-13 - 12.566370614358764 %i] +--R , +--R +--R [1. + 8.9000000000000004 %i, - 11.968123136900999 + 11.331887275852999 %i, +--R - 11.968123136900861 - 1.2344833385062608 %i, +--R 1.3855583347321954E-13 - 12.56637061435926 %i] +--R , +--R +--R [1. + 9. %i, - 12.119616119281 + 11.551156276202001 %i, +--R - 12.119616119281286 - 1.0152143381569982 %i, +--R - 2.8599345114344032E-13 - 12.566370614358998 %i] +--R , +--R +--R [1. + 9.0999999999999996 %i, - 12.271170833867 + 11.771534118309001 %i, +--R - 12.271170833867483 - 0.79483649604973161 %i, +--R - 4.8316906031686813E-13 - 12.566370614358732 %i] +--R , +--R +--R [1. + 9.1999999999999993 %i, - 12.422785931281 + 11.993008666285 %i, +--R - 12.422785931280877 - 0.5733619480744393 %i, +--R 1.2256862191861728E-13 - 12.566370614359439 %i] +--R , +--R +--R [1. + 9.3000000000000007 %i, - 12.574460105908001 + 12.215568046479 %i, +--R - 12.574460105908262 - 0.35080256788055886 %i, +--R - 2.6112445539183682E-13 - 12.566370614359558 %i] +--R , +--R +--R [1. + 9.4000000000000004 %i, - 12.726192094029001 + 12.43920063909 %i, +--R - 12.726192094029377 - 0.12716997526913024 %i, +--R - 3.765876499528531E-13 - 12.56637061435913 %i] +--R , +--R +--R [1. + 9.5 %i, - 12.877980672044 + 12.663895070128 %i, +--R - 12.877980672043599 + 9.7524455768741289E-2 %i, +--R 4.0145664570445661E-13 - 12.566370614359258 %i] +--R , +--R +--R [1. + 9.5999999999999996 %i, - 13.029824654789 + 12.889640203708 %i, +--R - 13.02982465478944 + 0.32326958934851951 %i, +--R - 4.4053649617126212E-13 - 12.56637061435948 %i] +--R , +--R +--R [1. + 9.6999999999999993 %i, - 13.181722893950999 + 13.116425134666001 %i, +--R - 13.181722893951155 + 0.55005452030683832 %i, +--R - 1.5631940186722204E-13 - 12.566370614359162 %i] +--R , +--R +--R [1. + 9.8000000000000007 %i, - 13.333674276547001 + 13.344239181477 %i, +--R - 13.333674276547052 + 0.77786856711780805 %i, +--R - 5.1514348342607263E-14 - 12.566370614359192 %i] +--R , +--R +--R [1. + 9.9000000000000004 %i, - 13.485677723495 + 13.573071879455 %i, +--R - 13.485677723494533 + 1.0067012650958465 %i, +--R 4.6718184876226587E-13 - 12.566370614359153 %i] +--R , +--R +--R [1. + 10. %i, - 13.637732188247 + 13.802912974230001 %i, +--R - 13.637732188247268 + 1.2365423598707301 %i, +--R - 2.6822988274943782E-13 - 12.56637061435927 %i] +--R ] +--R Type: List List Complex DoubleFloat +--E 4 )spool )lisp (bye) @@ -1592,5 +2416,7 @@ close(viewport) http://dlmf.nist.gov \bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', Dover Publications, Inc. New York 1965. pp267-270 +\bibitem{3} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp277 \end{thebibliography} \end{document} diff --git a/src/input/log.input.pamphlet b/src/input/log.input.pamphlet new file mode 100644 index 0000000..8c6f78e --- /dev/null +++ b/src/input/log.input.pamphlet @@ -0,0 +1,442 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input log.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This compares Axiom's log function with the tables published in +Abramowitz and Stegun. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of log(x), ranging from 0.01 to 2.00. The +second column is the reference value of log from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp100-113 + +<<*>>= +)spool log.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +[[0.01, -4.6051701859880914, log(0.01), log(0.01)-(-4.6051701859880914)], _ +[0.02, -3.9120230054281461, log(0.02), log(0.02)-(-3.9120230054281461)], _ +[0.03, -3.5065578973199817, log(0.03), log(0.03)-(-3.5065578973199817)], _ +[0.04, -3.2188758248682007, log(0.04), log(0.04)-(-3.2188758248682007)], _ +[0.05, -2.9957322735539910, log(0.05), log(0.05)-(-2.9957322735539910)], _ +[0.06, -2.8134107167600364, log(0.06), log(0.06)-(-2.8134107167600364)], _ +[0.07, -2.6592600369327781, log(0.07), log(0.07)-(-2.6592600369327781)], _ +[0.08, -2.5257286443082554, log(0.08), log(0.08)-(-2.5257286443082554)], _ +[0.09, -2.4079456086518720, log(0.09), log(0.09)-(-2.4079456086518720)], _ +[0.10, -2.3025850929940457, log(0.10), log(0.10)-(-2.3025850929940457)], _ +[0.11, -2.2072749131897208, log(0.11), log(0.11)-(-2.2072749131897208)], _ +[0.12, -2.1202635362000911, log(0.12), log(0.12)-(-2.1202635362000911)], _ +[0.13, -2.0402208285265546, log(0.13), log(0.13)-(-2.0402208285265546)], _ +[0.14, -1.9661128563728328, log(0.14), log(0.14)-(-1.9661128563728328)], _ +[0.15, -1.8971199848858813, log(0.15), log(0.15)-(-1.8971199848858813)], _ +[0.16, -1.8325814637483101, log(0.16), log(0.16)-(-1.8325814637483101)], _ +[0.17, -1.7719568419318753, log(0.17), log(0.17)-(-1.7719568419318753)], _ +[0.18, -1.7147984280919267, log(0.18), log(0.18)-(-1.7147984280919267)], _ +[0.19, -1.6607312068216509, log(0.19), log(0.19)-(-1.6607312068216509)], _ +[0.20, -1.6094379124341004, log(0.20), log(0.20)-(-1.6094379124341004)], _ +[0.21, -1.5606477482646684, log(0.21), log(0.21)-(-1.5606477482646684)], _ +[0.22, -1.5141277326297755, log(0.22), log(0.22)-(-1.5141277326297755)], _ +[0.23, -1.4696759700589417, log(0.23), log(0.23)-(-1.4696759700589417)], _ +[0.24, -1.4271163556401457, log(0.24), log(0.24)-(-1.4271163556401457)], _ +[0.25, -1.3862943611198906, log(0.25), log(0.25)-(-1.3862943611198906)], _ +[0.26, -1.3470736479666093, log(0.26), log(0.26)-(-1.3470736479666093)], _ +[0.27, -1.3093333199837623, log(0.27), log(0.27)-(-1.3093333199837623)], _ +[0.28, -1.2729656758128874, log(0.28), log(0.28)-(-1.2729656758128874)], _ +[0.29, -1.2378743560016173, log(0.29), log(0.29)-(-1.2378743560016173)], _ +[0.30, -1.2039728043259360, log(0.30), log(0.30)-(-1.2039728043259360)], _ +[0.31, -1.1711829815029451, log(0.31), log(0.31)-(-1.1711829815029451)], _ +[0.32, -1.1394342831883648, log(0.32), log(0.32)-(-1.1394342831883648)], _ +[0.33, -1.1086626245216111, log(0.33), log(0.33)-(-1.1086626245216111)], _ +[0.34, -1.0788096613719300, log(0.34), log(0.34)-(-1.0788096613719300)], _ +[0.35, -1.0498221244986777, log(0.35), log(0.35)-(-1.0498221244986777)], _ +[0.36, -1.0216512475319814, log(0.36), log(0.36)-(-1.0216512475319814)], _ +[0.37, -0.9942522733438669, log(0.37), log(0.37)-(-0.9942522733438669)], _ +[0.38, -0.9675840262617056, log(0.38), log(0.38)-(-0.9675840262617056)], _ +[0.39, -0.9416085398584449, log(0.39), log(0.39)-(-0.9416085398584449)], _ +[0.40, -0.9162907318741551, log(0.40), log(0.40)-(-0.9162907318741551)], _ +[0.41, -0.8915981192837836, log(0.41), log(0.41)-(-0.8915981192837836)], _ +[0.42, -0.8675005677047231, log(0.42), log(0.42)-(-0.8675005677047231)], _ +[0.43, -0.8439700702945289, log(0.43), log(0.43)-(-0.8439700702945289)], _ +[0.44, -0.8209805520698302, log(0.44), log(0.44)-(-0.8209805520698302)], _ +[0.45, -0.7985076962177716, log(0.45), log(0.45)-(-0.7985076962177716)], _ +[0.46, -0.7765287894989964, log(0.46), log(0.46)-(-0.7765287894989964)], _ +[0.47, -0.7550225842780328, log(0.47), log(0.47)-(-0.7550225842780328)], _ +[0.48, -0.7339691750802004, log(0.48), log(0.48)-(-0.7339691750802004)], _ +[0.49, -0.7133498878774648, log(0.49), log(0.49)-(-0.7133498878774648)], _ +[0.50, -0.6931471805599453, log(0.50), log(0.50)-(-0.6931471805599453)], _ +[0.51, -0.6733445532637656, log(0.51), 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[1.91,0.6471032420 585385,0.6471032420 5853850481,0.481 E -17], +--R [1.92,0.6523251860 396902,0.6523251860 3969017986,- 0.201 E -16], +--R [1.93,0.6575200029 167942,0.6575200029 1679418382,- 0.162 E -16], +--R [1.94,0.6626879730 752368,0.6626879730 752367635,- 0.365 E -16], +--R [1.95,0.6678293725 756554,0.6678293725 7565543401,0.34 E -16], +--R [1.96,0.6729444732 424259,0.6729444732 4242586101,- 0.39 E -16], +--R [1.97,0.6780335427 498971,0.6780335427 4989713874,0.387 E -16], +--R [1.98,0.6830968447 064439,0.6830968447 0644386823,- 0.318 E -16], +--R [1.99,0.6881346387 36401,0.6881346387 3640102737,0.274 E -16], +--R [2.0,0.6931471805 599453,0.6931471805 5994530942,0.942 E -17]] +--R Type: List List Float +--E 1 +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp100-113 +\end{thebibliography} +\end{document} + diff --git a/src/input/seccsc.input.pamphlet b/src/input/seccsc.input.pamphlet new file mode 100644 index 0000000..05d789e --- /dev/null +++ b/src/input/seccsc.input.pamphlet @@ -0,0 +1,695 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input seccsc.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This compares Axiom's sec and csc functions with the tables published in +Abramowitz and Stegun. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of sec(x), ranging from 0.01 to 1.60. The +second column is the reference value of sec from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp186-188 +<<*>>= +)spool seccsc.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.01,1.0000500,sec(0.01),sec(0.01)-1.0000500],_ +[0.02,1.0002000,sec(0.02),sec(0.02)-1.0002000],_ +[0.03,1.0004502,sec(0.03),sec(0.03)-1.0004502],_ +[0.04,1.0008005,sec(0.04),sec(0.04)-1.0008005],_ +[0.05,1.0012513,sec(0.05),sec(0.05)-1.0012513],_ +[0.06,1.0018027,sec(0.06),sec(0.06)-1.0018027],_ +[0.07,1.0024550,sec(0.07),sec(0.07)-1.0024550],_ +[0.08,1.0032086,sec(0.08),sec(0.08)-1.0032086],_ +[0.09,1.0040637,sec(0.09),sec(0.09)-1.0040637],_ +[0.10,1.0050209,sec(0.10),sec(0.10)-1.0050209],_ +[0.11,1.0060807,sec(0.11),sec(0.11)-1.0060807],_ +[0.12,1.0072435,sec(0.12),sec(0.12)-1.0072435],_ +[0.13,1.0085099,sec(0.13),sec(0.13)-1.0085099],_ +[0.14,1.0098807,sec(0.14),sec(0.14)-1.0098807],_ +[0.15,1.0113564,sec(0.15),sec(0.15)-1.0113564],_ +[0.16,1.0129380,sec(0.16),sec(0.16)-1.0129380],_ +[0.17,1.0146261,sec(0.17),sec(0.17)-1.0146261],_ +[0.18,1.0164216,sec(0.18),sec(0.18)-1.0164216],_ +[0.19,1.0183255,sec(0.19),sec(0.19)-1.0183255],_ +[0.20,1.0203388,sec(0.20),sec(0.20)-1.0203388],_ +[0.21,1.0224626,sec(0.21),sec(0.21)-1.0224626],_ +[0.22,1.0246978,sec(0.22),sec(0.22)-1.0246978],_ +[0.23,1.0270458,sec(0.23),sec(0.23)-1.0270458],_ +[0.24,1.0295078,sec(0.24),sec(0.24)-1.0295078],_ +[0.25,1.0320850,sec(0.25),sec(0.25)-1.0320850],_ +[0.26,1.0347789,sec(0.26),sec(0.26)-1.0347789],_ +[0.27,1.0375910,sec(0.27),sec(0.27)-1.0375910],_ +[0.28,1.0405227,sec(0.28),sec(0.28)-1.0405227],_ +[0.29,1.0435757,sec(0.29),sec(0.29)-1.0435757],_ +[0.30,1.0467516,sec(0.30),sec(0.30)-1.0467516],_ +[0.31,1.0500522,sec(0.31),sec(0.31)-1.0500522],_ +[0.32,1.0534794,sec(0.32),sec(0.32)-1.0534794],_ +[0.33,1.0570351,sec(0.33),sec(0.33)-1.0570351],_ +[0.34,1.0607213,sec(0.34),sec(0.34)-1.0607213],_ +[0.35,1.0645402,sec(0.35),sec(0.35)-1.0645402],_ +[0.36,1.0684938,sec(0.36),sec(0.36)-1.0684938],_ +[0.37,1.0725847,sec(0.37),sec(0.37)-1.0725847],_ +[0.38,1.0768150,sec(0.38),sec(0.38)-1.0768150],_ +[0.39,1.0811874,sec(0.39),sec(0.39)-1.0811874],_ +[0.40,1.0857044,sec(0.40),sec(0.40)-1.0857044],_ +[0.41,1.0903689,sec(0.41),sec(0.41)-1.0903689],_ +[0.42,1.0951836,sec(0.42),sec(0.42)-1.0951836],_ +[0.43,1.1001515,sec(0.43),sec(0.43)-1.1001515],_ +[0.44,1.1052757,sec(0.44),sec(0.44)-1.1052757],_ +[0.45,1.1105594,sec(0.45),sec(0.45)-1.1105594],_ +[0.46,1.1160060,sec(0.46),sec(0.46)-1.1160060],_ +[0.47,1.1216191,sec(0.47),sec(0.47)-1.1216191],_ +[0.48,1.1274022,sec(0.48),sec(0.48)-1.1274022],_ +[0.49,1.1333591,sec(0.49),sec(0.49)-1.1333591],_ +[0.50,1.1394939,sec(0.50),sec(0.50)-1.1394939],_ +[0.51,1.1458107,sec(0.51),sec(0.51)-1.1458107],_ +[0.52,1.1523138,sec(0.52),sec(0.52)-1.1523138],_ +[0.53,1.1590077,sec(0.53),sec(0.53)-1.1590077],_ +[0.54,1.1658970,sec(0.54),sec(0.54)-1.1658970],_ +[0.55,1.1729868,sec(0.55),sec(0.55)-1.1729868],_ +[0.56,1.1802821,sec(0.56),sec(0.56)-1.1802821],_ +[0.57,1.1877881,sec(0.57),sec(0.57)-1.1877881],_ +[0.58,1.1955106,sec(0.58),sec(0.58)-1.1955106],_ +[0.59,1.2034553,sec(0.59),sec(0.59)-1.2034553],_ +[0.60,1.2116283,sec(0.60),sec(0.60)-1.2116283],_ +[0.61,1.2200359,sec(0.61),sec(0.61)-1.2200359],_ +[0.62,1.2286847,sec(0.62),sec(0.62)-1.2286847],_ +[0.63,1.2375816,sec(0.63),sec(0.63)-1.2375816],_ +[0.64,1.2467339,sec(0.64),sec(0.64)-1.2467339],_ +[0.65,1.2561492,sec(0.65),sec(0.65)-1.2561492],_ +[0.66,1.2658352,sec(0.66),sec(0.66)-1.2658352],_ +[0.67,1.2758004,sec(0.67),sec(0.67)-1.2758004],_ +[0.68,1.2860534,sec(0.68),sec(0.68)-1.2860534],_ +[0.69,1.2966031,sec(0.69),sec(0.69)-1.2966031],_ +[0.70,1.3074593,sec(0.70),sec(0.70)-1.3074593],_ +[0.71,1.3186317,sec(0.71),sec(0.71)-1.3186317],_ +[0.72,1.3301309,sec(0.72),sec(0.72)-1.3301309],_ +[0.73,1.3419677,sec(0.73),sec(0.73)-1.3419677],_ +[0.74,1.3541538,sec(0.74),sec(0.74)-1.3541538],_ +[0.75,1.3667011,sec(0.75),sec(0.75)-1.3667011],_ +[0.76,1.3796224,sec(0.76),sec(0.76)-1.3796224],_ +[0.77,1.3929310,sec(0.77),sec(0.77)-1.3929310],_ +[0.78,1.4066408,sec(0.78),sec(0.78)-1.4066408],_ +[0.79,1.4207667,sec(0.79),sec(0.79)-1.4207667],_ +[0.80,1.4353242,sec(0.80),sec(0.80)-1.4353242],_ +[0.81,1.4503296,sec(0.81),sec(0.81)-1.4503296],_ +[0.82,1.4658002,sec(0.82),sec(0.82)-1.4658002],_ +[0.83,1.4817542,sec(0.83),sec(0.83)-1.4817542],_ +[0.84,1.4982108,sec(0.84),sec(0.84)-1.4982108],_ +[0.85,1.5151902,sec(0.85),sec(0.85)-1.5151902],_ +[0.86,1.5327139,sec(0.86),sec(0.86)-1.5327139],_ +[0.87,1.5508046,sec(0.87),sec(0.87)-1.5508046],_ +[0.88,1.5694863,sec(0.88),sec(0.88)-1.5694863],_ +[0.89,1.5887844,sec(0.89),sec(0.89)-1.5887844],_ +[0.90,1.6087258,sec(0.90),sec(0.90)-1.6087258],_ +[0.91,1.6293392,sec(0.91),sec(0.91)-1.6293392],_ +[0.92,1.6506549,sec(0.92),sec(0.92)-1.6506549],_ +[0.93,1.6727052,sec(0.93),sec(0.93)-1.6727052],_ +[0.94,1.6955244,sec(0.94),sec(0.94)-1.6955244],_ +[0.95,1.7191492,sec(0.95),sec(0.95)-1.7191492],_ +[0.96,1.7436184,sec(0.96),sec(0.96)-1.7436184],_ +[0.97,1.7689737,sec(0.97),sec(0.97)-1.7689737],_ +[0.98,1.7952595,sec(0.98),sec(0.98)-1.7952595],_ +[0.99,1.8225232,sec(0.99),sec(0.99)-1.8225232],_ +[1.00,1.8508157,sec(1.00),sec(1.00)-1.8508157],_ +[1.01,1.8801915,sec(1.01),sec(1.01)-1.8801915],_ +[1.02,1.9107089,sec(1.02),sec(1.02)-1.9107089],_ +[1.03,1.9424308,sec(1.03),sec(1.03)-1.9424308],_ +[1.04,1.9754247,sec(1.04),sec(1.04)-1.9754247],_ +[1.05,2.0097632,sec(1.05),sec(1.05)-2.0097632],_ +[1.06,2.0455249,sec(1.06),sec(1.06)-2.0455249],_ +[1.07,2.0827943,sec(1.07),sec(1.07)-2.0827943],_ +[1.08,2.1216631,sec(1.08),sec(1.08)-2.1216631],_ +[1.09,2.1622306,sec(1.09),sec(1.09)-2.1622306],_ +[1.10,2.2046044,sec(1.10),sec(1.10)-2.2046044],_ +[1.11,2.2489016,sec(1.11),sec(1.11)-2.2489016],_ +[1.12,2.2952497,sec(1.12),sec(1.12)-2.2952497],_ +[1.13,2.3437877,sec(1.13),sec(1.13)-2.3437877],_ +[1.14,2.3946675,sec(1.14),sec(1.14)-2.3946675],_ +[1.15,2.4480557,sec(1.15),sec(1.15)-2.4480557],_ +[1.16,2.5041348,sec(1.16),sec(1.16)-2.5041348],_ +[1.17,2.5631057,sec(1.17),sec(1.17)-2.5631057],_ +[1.18,2.6251899,sec(1.18),sec(1.18)-2.6251899],_ +[1.19,2.6906321,sec(1.19),sec(1.19)-2.6906321],_ +[1.20,2.7597036,sec(1.20),sec(1.20)-2.7597036],_ +[1.21,2.8327055,sec(1.21),sec(1.21)-2.8327055],_ +[1.22,2.9099735,sec(1.22),sec(1.22)-2.9099735],_ +[1.23,2.9918825,sec(1.23),sec(1.23)-2.9918825],_ +[1.24,3.0788530,sec(1.24),sec(1.24)-3.0788530],_ +[1.25,3.1713577,sec(1.25),sec(1.25)-3.1713577],_ +[1.26,3.2699304,sec(1.26),sec(1.26)-3.2699304],_ +[1.27,3.3751757,sec(1.27),sec(1.27)-3.3751757],_ +[1.28,3.4877815,sec(1.28),sec(1.28)-3.4877815],_ +[1.29,3.6085336,sec(1.29),sec(1.29)-3.6085336],_ +[1.30,3.7383341,sec(1.30),sec(1.30)-3.7383341],_ +[1.31,3.8782233,sec(1.31),sec(1.31)-3.8782233],_ +[1.32,4.0294074,sec(1.32),sec(1.32)-4.0294074],_ +[1.33,4.1932931,sec(1.33),sec(1.33)-4.1932931],_ +[1.34,4.3715310,sec(1.34),sec(1.34)-4.3715310],_ +[1.35,4.5660706,sec(1.35),sec(1.35)-4.5660706],_ +[1.36,4.7792314,sec(1.36),sec(1.36)-4.7792314],_ +[1.37,5.0137949,sec(1.37),sec(1.37)-5.0137949],_ +[1.38,5.2731260,sec(1.38),sec(1.38)-5.2731260],_ +[1.39,5.5613339,sec(1.39),sec(1.39)-5.5613339],_ +[1.40,5.8834901,sec(1.40),sec(1.40)-5.8834901],_ +[1.41,6.2459280,sec(1.41),sec(1.41)-6.2459280],_ +[1.42,6.6566608,sec(1.42),sec(1.42)-6.6566608],_ +[1.43,7.1259785,sec(1.43),sec(1.43)-7.1259785],_ +[1.44,7.6673176,sec(1.44),sec(1.44)-7.6673176],_ +[1.45,8.2985645,sec(1.45),sec(1.45)-8.2985645],_ +[1.46,9.0440625,sec(1.46),sec(1.46)-9.0440625],_ +[1.47,9.9378158,sec(1.47),sec(1.47)-9.9378158],_ +[1.48,11.0288087,sec(1.48),sec(1.48)-11.0288087],_ +[1.49,12.3902766,sec(1.49),sec(1.49)-12.3902766],_ +[1.50,14.1368329,sec(1.50),sec(1.50)-14.1368329],_ +[1.51,16.4584992,sec(1.51),sec(1.51)-16.4584992],_ +[1.52,19.6949314,sec(1.52),sec(1.52)-19.6949314],_ +[1.53,24.5188114,sec(1.53),sec(1.53)-24.5188114],_ +[1.54,32.4765383,sec(1.54),sec(1.54)-32.4765383],_ +[1.55,48.0888810,sec(1.55),sec(1.55)-48.0888810],_ +[1.56,92.6258945,sec(1.56),sec(1.56)-92.6258945],_ +[1.57,1255.7659897,sec(1.57),sec(1.57)-1255.7659897],_ +[1.58,-108.6538055,sec(1.58),sec(1.58)-(-108.6538055)],_ +[1.59,-52.0765718,sec(1.59),sec(1.59)-(-52.0765718)],_ +[1.60,-34.2471356,sec(1.60),sec(1.60)-(-34.2471356)]] +--R +--R +--R (1) +--R [[0.01,1.00005,1.0000500020 83418059,0.2083418059 E -8], +--R [0.02,1.0002,1.0002000333 387564351,0.3333875643 51 E -7], +--R [0.03,1.0004502,1.0004501688 117850454,- 0.3118821495 46 E -7], +--R [0.04,1.0008005,1.0008005336 805808191,0.3368058081 91 E -7], +--R [0.05,1.0012513,1.0012513034 084612212,0.3408461221 2 E -8], +--R [0.06,1.0018027,1.0018027039 585779448,0.3958577944 8 E -8], +--R [0.07,1.002455,1.0024550120 706596665,0.1207065966 65 E -7], +--R [0.08,1.0032086,1.0032085556 00535503,- 0.4439946449 7 E -7], +--R [0.09,1.0040637,1.0040637139 232158779,0.1392321587 79 E -7], +--R [0.1,1.0050209,1.0050209184 004554285,0.1840045542 85 E -7], +--R [0.11,1.0060807,1.0060806529 138739295,- 0.4708612607 05 E -7], +--R [0.12,1.0072435,1.0072434544 648665414,- 0.4553513345 86 E -7], +--R [0.13,1.0085099,1.0085099138 426946141,0.1384269461 41 E -7], +--R [0.14,1.0098807,1.0098806763 623134089,- 0.2363768659 11 E -7], +--R [0.15,1.0113564,1.0113564426 736640909,0.4267366409 09 E -7], +--R [0.16,1.012938,1.0129379696 44334881,- 0.3035566511 9 E -7], +--R [0.17,1.0146261,1.0146260713 176810517,- 0.2868231894 83 E -7], +--R [0.18,1.0164216,1.0164216199 486862747,0.1994868627 47 E -7], +--R [0.19,1.0183255,1.0183255471 200494754,0.4712004947 54 E -7], +--R [0.2,1.0203388,1.0203388449 411926898,0.4494119268 98 E -7], +--R [0.21,1.0224626,1.0224625673 331073524,- 0.3266689264 76 E -7], +--R [0.22,1.0246978,1.0246978314 021899569,0.3140218995 69 E -7], +--R [0.23,1.0270458,1.0270458189 064641552,0.1890646415 52 E -7], +--R [0.24,1.0295078,1.0295077778 178462266,- 0.2218215377 34 E -7], +--R [0.25,1.032085,1.0320850239 843856444,0.2398438564 44 E -7], +--R [0.26,1.0347789,1.0347789428 967034948,0.4289670349 48 E -7], +--R [0.27,1.037591,1.0375909915 631601515,- 0.8436839848 51 E -8], +--R [0.28,1.0405227,1.0405227004 986113757,0.4986113757 E -9], +--R [0.29,1.0435757,1.0435756758 319605292,- 0.2416803947 08 E -7], +--R [0.3,1.0467516,1.0467516015 380856009,0.1538085600 9 E -8], +--R [0.31,1.0500522,1.0500522418 001151664,0.4180011516 64 E -7], +--R [0.32,1.0534794,1.0534794435 08449282,0.4350844928 2 E -7], +--R [0.33,1.0570351,1.0570351389 033719014,0.3890337190 14 E -7], +--R [0.34,1.0607213,1.0607213483 685831203,0.4836858312 03 E -7], +--R [0.35,1.0645402,1.0645401833 834950584,- 0.1661650494 16 E -7], +--R [0.36,1.0684938,1.0684938496 426873472,0.4964268734 72 E -7], +--R [0.37,1.0725847,1.0725846503 515101556,- 0.4964848984 44 E -7], +--R [0.38,1.076815,1.0768149897 074578722,- 0.1029254212 78 E -7], +--R [0.39,1.0811874,1.0811873765 776187103,- 0.2342238128 97 E -7], +--R [0.4,1.0857044,1.0857044283 832387031,0.2838323870 31 E -7], +--R [0.41,1.0903689,1.0903688752 032272686,- 0.2479677273 14 E -7], +--R [0.42,1.0951836,1.0951835641 092806502,- 0.3589071934 98 E -7], +--R [0.43,1.1001515,1.1001514637 462144293,- 0.3625378557 07 E -7], +--R [0.44,1.1052757,1.1052756691 720828447,- 0.3082791715 53 E -7], +--R [0.45,1.1105594,1.1105594069 737272884,0.6973727288 4 E -8], +--R [0.46,1.116006,1.1160060406 745461642,0.4067454616 42 E -7], +--R [0.47,1.1216191,1.1216190764 525210869,- 0.2354747891 32 E -7], +--R [0.48,1.1274022,1.1274021691 878787428,- 0.3081212125 72 E -7], +--R [0.49,1.1333591,1.1333591288 612230659,0.2886122306 59 E -7], +--R [0.5,1.1394939,1.1394939273 245491223,0.2732454912 23 E -7], +--R [0.51,1.1458107,1.1458107054 692597334,0.5469259733 4 E -8], +--R [0.52,1.1523138,1.1523137808 171610842,- 0.1918283891 58 E -7], +--R [0.53,1.1590077,1.1590076555 624283961,- 0.4443757160 39 E -7], +--R [0.54,1.165897,1.1658970250 947227087,0.2509472270 87 E -7], +--R [0.55,1.1729868,1.1729867870 360221145,- 0.1296397788 55 E -7], +--R [0.56,1.1802821,1.1802820508 263244778,- 0.4917367552 22 E -7], +--R [0.57,1.1877881,1.1877881478 962049114,0.4789620491 14 E -7], +--R [0.58,1.1955106,1.1955106424 672935752,0.4246729357 52 E -7], +--R [0.59,1.2034553,1.2034553430 251038492,0.4302510384 92 E -7], +--R [0.6,1.2116283,1.2116283145 123167046,0.1451231670 46 E -7], +--R [0.61,1.2200359,1.2200358912 946465932,- 0.8705353406 83 E -8], +--R [0.62,1.2286847,1.2286846909 558135602,- 0.9044186439 82 E -8], +--R [0.63,1.2375816,1.2375816289 829659823,0.2898296598 23 E -7], +--R [0.64,1.2467339,1.2467339344 091835044,0.3440918350 44 E -7], +--R [0.65,1.2561492,1.2561491664 854909887,- 0.3351450901 13 E -7], +--R [0.66,1.2658352,1.2658352324 611882698,0.3246118826 98 E -7], +--R [0.67,1.2758004,1.2758004065 583108419,0.6558310841 9 E -8], +--R [0.68,1.2860534,1.2860533502 337547427,- 0.4976624525 73 E -7], +--R [0.69,1.2966031,1.2966031338 311052265,0.3383110522 65 E -7], +--R [0.7,1.3074593,1.3074592597 335938699,- 0.4026640613 01 E -7], +--R [0.71,1.3186317,1.3186316871 399746265,- 0.1286002537 35 E -7], +--R [0.72,1.3301309,1.3301308585 965713491,- 0.4140342865 09 E -7], +--R [0.73,1.3419677,1.3419677284 314378096,0.2843143780 96 E -7], +--R [0.74,1.3541538,1.3541537932 506339213,- 0.6749366078 7 E -8], +--R [0.75,1.3667011,1.3667011246 722261352,0.2467222613 52 E -7], +--R [0.76,1.3796224,1.3796224044 909559952,0.4490955995 2 E -8], +--R [0.77,1.392931,1.3929309624 858048639,- 0.3751419513 61 E -7], +--R [0.78,1.4066408,1.4066408171 041612211,0.1710416122 11 E -7], +--R [0.79,1.4207667,1.4207667192 802507471,0.1928025074 71 E -7], +--R [0.8,1.4353242,1.4353241996 722398005,- 0.3277601995 E -9], +--R [0.81,1.4503296,1.4503296196 323374816,0.1963233748 16 E -7], +--R [0.82,1.4658002,1.4658002262 577216995,0.2625772169 95 E -7], +--R [0.83,1.4817542,1.4817542119 076845659,0.1190768456 59 E -7], +--R [0.84,1.4982108,1.4982107786 145889242,- 0.2138541107 58 E -7], +--R [0.85,1.5151902,1.5151902078 636927634,0.7863692763 37 E -8], +--R [0.86,1.5327139,1.5327139362 703728857,0.3627037288 57 E -7], +--R [0.87,1.5508046,1.5508046377 436210518,0.3774362105 18 E -7], +--R [0.88,1.5694863,1.5694863127 928890316,0.1279288903 16 E -7], +--R [0.89,1.5887844,1.5887843857 125782891,- 0.1428742171 09 E -7], +--R [0.9,1.6087258,1.6087258104 66049513,0.1046604951 3 E -7], +--R [0.91,1.6293392,1.6293391861 905347268,- 0.1380946527 32 E -7], +--R [0.92,1.6506549,1.6506548833 576031068,- 0.1664239689 32 E -7], +--R [0.93,1.6727052,1.6727051817 530083925,- 0.1824699160 75 E -7], +--R [0.94,1.6955244,1.6955244215 873528318,0.2158735283 18 E -7], +--R [0.95,1.7191492,1.7191491692 180088055,- 0.3078199119 45 E -7], +--R [0.96,1.7436184,1.7436183991 566481012,- 0.8433518988 E -9], +--R [0.97,1.7689737,1.7689736942 596852048,- 0.5740314795 2 E -8], +--R [0.98,1.7952595,1.7952594662 558616387,- 0.3374413836 13 E -7], +--R [0.99,1.8225232,1.8225231990 619311821,- 0.9380688178 8 E -9], +--R [1.0,1.8508157,1.8508157176 809256179,0.1768092561 79 E -7], +--R [1.01,1.8801915,1.8801914858 76130416,- 0.1412386958 4 E -7], +--R [1.02,1.9107089,1.9107089362 776886454,0.3627768864 54 E -7], +--R [1.03,1.9424308,1.9424308371 197244332,0.3711972443 32 E -7], +--R [1.04,1.9754247,1.9754247004 385756762,0.4385756762 E -9], +--R [1.05,2.0097632,2.0097632373 047619814,0.3730476198 15 E -7], +--R [1.06,2.0455249,2.0455248665 340933506,- 0.3346590664 94 E -7], +--R [1.07,2.0827943,2.0827942843 529550117,- 0.1564704498 83 E -7], +--R [1.08,2.1216631,2.1216631037 112423848,0.3711242384 8 E -8], +--R [1.09,2.1622306,2.1622305733 829374458,- 0.2661706255 42 E -7], +--R [1.1,2.2046044,2.2046043887 17359034,- 0.1128264096 6 E -7], +--R [1.11,2.2489016,2.2489016079 636949635,0.7963694963 5 E -8], +--R [1.12,2.2952497,2.2952496905 621863932,- 0.9437813606 7 E -8], +--R [1.13,2.3437877,2.3437876767 70567607,- 0.2322943239 29 E -7], +--R [1.14,2.3946675,2.3946675315 911689408,0.3159116894 08 E -7], +--R [1.15,2.4480557,2.4480556803 301802962,- 0.1966981970 38 E -7], +--R [1.16,2.5041348,2.5041347684 432143166,- 0.3155678568 34 E -7], +--R [1.17,2.5631057,2.5631056848 391647153,- 0.1516083528 47 E -7], +--R [1.18,2.6251899,2.6251898958 332672918,- 0.4166732708 2 E -8], +--R [1.19,2.6906321,2.6906321468 544274307,0.4685442743 07 E -7], +--R [1.2,2.7597036,2.7597036013 324064569,0.1332406457 E -8], +--R [1.21,2.8327055,2.8327055015 843215452,0.1584321545 E -8], +--R [1.22,2.9099735,2.9099734558 632119939,- 0.4413678800 61 E -7], +--R [1.23,2.9918825,2.9918824801 830430638,- 0.1981695693 62 E -7], +--R [1.24,3.078853,3.0788529546 387066657,- 0.4536129333 43 E -7], +--R [1.25,3.1713577,3.1713576937 701033609,- 0.6229896639 1 E -8], +--R [1.26,3.2699304,3.2699303818 839873852,- 0.1811601261 48 E -7], +--R [1.27,3.3751757,3.3751756909 804379951,- 0.9019562004 9 E -8], +--R [1.28,3.4877815,3.4877814863 175858326,- 0.1368241416 7 E -7], +--R [1.29,3.6085336,3.6085336400 439333502,0.4004393335 02 E -7], +--R [1.3,3.7383341,3.7383341270 754411719,0.2707544117 19 E -7], +--R [1.31,3.8782233,3.8782232842 002831965,- 0.1579971680 35 E -7], +--R [1.32,4.0294074,4.0294073944 135738582,- 0.5586426141 8 E -8], +--R [1.33,4.1932931,4.1932931445 375416679,0.4453754166 79 E -7], +--R [1.34,4.371531,4.3715310407 788541477,0.4077885414 77 E -7], +--R [1.35,4.5660706,4.5660706221 959586487,0.2219595864 9 E -7], +--R [1.36,4.7792314,4.7792313898 566530439,- 0.1014334695 6 E -7], +--R [1.37,5.0137949,5.0137949303 632701112,0.3036327011 12 E -7], +--R [1.38,5.273126,5.2731260096 064537537,0.9606453753 8 E -8], +--R [1.39,5.5613339,5.5613338533 248644648,- 0.4667513553 52 E -7], +--R [1.4,5.8834901,5.8834900848 27344827,- 0.1517265517 3 E -7], +--R [1.41,6.245928,6.2459279846 284984955,- 0.1537150150 4 E -7], +--R [1.42,6.6566608,6.6566608218 158868243,0.2181588682 4 E -7], +--R [1.43,7.1259785,7.1259784562 869696006,- 0.4371303039 94 E -7], +--R [1.44,7.6673176,7.6673176194 346817373,0.1943468173 7 E -7], +--R [1.45,8.2985645,8.2985644666 089360285,- 0.3339106397 1 E -7], +--R [1.46,9.0440625,9.0440625062 951398291,0.6295139829 E -8], +--R [1.47,9.9378158,9.9378157688 028373544,- 0.3119716264 6 E -7], +--R [1.48,11.0288087,11.0288086918 92599526,- 0.8107400473 9 E -8], +--R [1.49,12.3902766,12.3902765961 36436494,- 0.3863563506 E -8], +--R [1.5,14.1368329,14.1368329029 69903082,0.2969903082 E -8], +--R [1.51,16.4584992,16.4584992338 68991507,0.3386899150 7 E -7], +--R [1.52,19.6949314,19.6949314465 35659932,0.4653565993 2 E -7], +--R [1.53,24.5188114,24.5188114348 30172969,0.3483017296 9 E -7], +--R [1.54,32.4765383,32.4765382933 55461787,- 0.6644538213 E -8], +--R [1.55,48.088881,48.0888810173 88679831,0.1738867983 E -7], +--R [1.56,92.6258945,92.6258945325 36624847,0.3253662485 E -7], +--R [1.57,1255.7659897,1255.7659896641 100942,- 0.358899058 E -7], +--R [1.58,- 108.6538055,- 108.6538054739 3097269,0.2606902731 E -7], +--R [1.59,- 52.0765718,- 52.0765717826 07291365,0.1739270863 E -7], +--R [1.6,- 34.2471356,- 34.2471356100 18689204,- 0.100186892 E -7]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of csc(x), ranging from 0.01 to 1.60. The +second column is the reference value of csc from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp186-188 +<<*>>= + +--S 2 of 2 +[[0.01,100.0016667,csc(0.01),csc(0.01)-100.0016667],_ +[0.02,50.0033335,csc(0.02),csc(0.02)-50.0033335],_ +[0.03,33.3383339,csc(0.03),csc(0.03)-33.3383339],_ +[0.04,25.0066679,csc(0.04),csc(0.04)-25.0066679],_ +[0.05,20.0083358,csc(0.05),csc(0.05)-20.0083358],_ +[0.06,16.6766709,csc(0.06),csc(0.06)-16.6766709],_ +[0.07,14.2973876,csc(0.07),csc(0.07)-14.2973876],_ +[0.08,12.5133432,csc(0.08),csc(0.08)-12.5133432],_ +[0.09,11.1261253,csc(0.09),csc(0.09)-11.1261253],_ +[0.10,10.0166861,csc(0.10),csc(0.10)-10.0166861],_ +[0.11,9.1092683,csc(0.11),csc(0.11)-9.1092683],_ +[0.12,8.3533670,csc(0.12),csc(0.12)-8.3533670],_ +[0.13,7.7140172,csc(0.13),csc(0.13)-7.7140172],_ +[0.14,7.1662439,csc(0.14),csc(0.14)-7.1662439],_ +[0.15,6.6917324,csc(0.15),csc(0.15)-6.6917324],_ +[0.16,6.2767465,csc(0.16),csc(0.16)-6.2767465],_ +[0.17,5.9107821,csc(0.17),csc(0.17)-5.9107821],_ +[0.18,5.5856693,csc(0.18),csc(0.18)-5.5856693],_ +[0.19,5.2949584,csc(0.19),csc(0.19)-5.2949584],_ +[0.20,5.0334895,csc(0.20),csc(0.20)-5.0334895],_ +[0.21,4.7970857,csc(0.21),csc(0.21)-4.7970857],_ +[0.22,4.5823293,csc(0.22),csc(0.22)-4.5823293],_ +[0.23,4.3863973,csc(0.23),csc(0.23)-4.3863973],_ +[0.24,4.2069371,csc(0.24),csc(0.24)-4.2069371],_ +[0.25,4.0419725,csc(0.25),csc(0.25)-4.0419725],_ +[0.26,3.8898314,csc(0.26),csc(0.26)-3.8898314],_ +[0.27,3.7490894,csc(0.27),csc(0.27)-3.7490894],_ +[0.28,3.6185256,csc(0.28),csc(0.28)-3.6185256],_ +[0.29,3.4970877,csc(0.29),csc(0.29)-3.4970877],_ +[0.30,3.3838634,csc(0.30),csc(0.30)-3.3838634],_ +[0.31,3.2780583,csc(0.31),csc(0.31)-3.2780583],_ +[0.32,3.1789774,csc(0.32),csc(0.32)-3.1789774],_ +[0.33,3.0860099,csc(0.33),csc(0.33)-3.0860099],_ +[0.34,2.9986168,csc(0.34),csc(0.34)-2.9986168],_ +[0.35,2.9163208,csc(0.35),csc(0.35)-2.9163208],_ +[0.36,2.8386975,csc(0.36),csc(0.36)-2.8386975],_ +[0.37,2.7653687,csc(0.37),csc(0.37)-2.7653687],_ +[0.38,2.6959957,csc(0.38),csc(0.38)-2.6959957],_ +[0.39,2.6302748,csc(0.39),csc(0.39)-2.6302748],_ +[0.40,2.5679325,csc(0.40),csc(0.40)-2.5679325],_ +[0.41,2.5087220,csc(0.41),csc(0.41)-2.5087220],_ +[0.42,2.4524203,csc(0.42),csc(0.42)-2.4524203],_ +[0.43,2.3988248,csc(0.43),csc(0.43)-2.3988248],_ +[0.44,2.3477515,csc(0.44),csc(0.44)-2.3477515],_ +[0.45,2.2990327,csc(0.45),csc(0.45)-2.2990327],_ +[0.46,2.2525155,csc(0.46),csc(0.46)-2.2525155],_ +[0.47,2.2080598,csc(0.47),csc(0.47)-2.2080598],_ +[0.48,2.1655372,csc(0.48),csc(0.48)-2.1655372],_ +[0.49,2.1248300,csc(0.49),csc(0.49)-2.1248300],_ +[0.50,2.0858296,csc(0.50),csc(0.50)-2.0858296],_ +[0.51,2.0484363,csc(0.51),csc(0.51)-2.0484363],_ +[0.52,2.0125578,csc(0.52),csc(0.52)-2.0125578],_ +[0.53,1.9781089,csc(0.53),csc(0.53)-1.9781089],_ +[0.54,1.9450107,csc(0.54),csc(0.54)-1.9450107],_ +[0.55,1.9131900,csc(0.55),csc(0.55)-1.9131900],_ +[0.56,1.8825790,csc(0.56),csc(0.56)-1.8825790],_ +[0.57,1.8531145,csc(0.57),csc(0.57)-1.8531145],_ +[0.58,1.8247378,csc(0.58),csc(0.58)-1.8247378],_ +[0.59,1.7973941,csc(0.59),csc(0.59)-1.7973941],_ +[0.60,1.7710322,csc(0.60),csc(0.60)-1.7710322],_ +[0.61,1.7456045,csc(0.61),csc(0.61)-1.7456045],_ +[0.62,1.7210662,csc(0.62),csc(0.62)-1.7210662],_ +[0.63,1.6973757,csc(0.63),csc(0.63)-1.6973757],_ +[0.64,1.6744937,csc(0.64),csc(0.64)-1.6744937],_ +[0.65,1.6523834,csc(0.65),csc(0.65)-1.6523834],_ +[0.66,1.6310105,csc(0.66),csc(0.66)-1.6310105],_ +[0.67,1.6103423,csc(0.67),csc(0.67)-1.6103423],_ +[0.68,1.5903484,csc(0.68),csc(0.68)-1.5903484],_ +[0.69,1.5710001,csc(0.69),csc(0.69)-1.5710001],_ +[0.70,1.5522703,csc(0.70),csc(0.70)-1.5522703],_ +[0.71,1.5341335,csc(0.71),csc(0.71)-1.5341335],_ +[0.72,1.5165654,csc(0.72),csc(0.72)-1.5165654],_ +[0.73,1.4995435,csc(0.73),csc(0.73)-1.4995435],_ +[0.74,1.4830460,csc(0.74),csc(0.74)-1.4830460],_ +[0.75,1.4670527,csc(0.75),csc(0.75)-1.4670527],_ +[0.76,1.4515443,csc(0.76),csc(0.76)-1.4515443],_ +[0.77,1.4365025,csc(0.77),csc(0.77)-1.4365025],_ +[0.78,1.4219099,csc(0.78),csc(0.78)-1.4219099],_ 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0.3976364529 23 E -7], +--R [0.74,1.483046,1.4830460145 509444868,0.1455094448 68 E -7], +--R [0.75,1.4670527,1.4670527244 75010117,0.2447501011 7 E -7], +--R [0.76,1.4515443,1.4515443046 478685727,0.4647868572 7 E -8], +--R [0.77,1.4365025,1.4365024847 353014963,- 0.1526469850 37 E -7], +--R [0.78,1.4219099,1.4219099446 09135172,0.4460913517 2 E -7], +--R [0.79,1.4077503,1.4077502544 566480148,- 0.4554335198 52 E -7], +--R [0.8,1.3940078,1.3940078193 886361745,0.1938863617 45 E -7], +--R [0.81,1.3806678,1.3806678281 575591498,0.2815755914 98 E -7], +--R [0.82,1.3677162,1.3677162056 35104192,0.5635104192 E -8], +--R [0.83,1.3551396,1.3551395687 323139549,- 0.3126768604 51 E -7], +--R [0.84,1.3429252,1.3429251854 756057525,- 0.1452439424 75 E -7], +--R [0.85,1.3310609,1.3310609369 789990246,0.3697899902 46 E -7], +--R [0.86,1.3195353,1.3195352820 770317831,- 0.1792296821 69 E -7], +--R [0.87,1.3083372,1.3083372244 045115315,0.2440451153 15 E -7], +--R [0.88,1.2974563,1.2974562817 286954688,- 0.1827130453 12 E -7], +--R [0.89,1.2868825,1.2868824573 569776297,- 0.4264302237 03 E -7], +--R [0.9,1.2766062,1.2766062134 58895496,0.1345889549 6 E -7], +--R [0.91,1.2666184,1.2666184461 554476329,0.4615544763 29 E -7], +--R [0.92,1.2569105,1.2569104622 415061901,- 0.3775849380 99 E -7], +--R [0.93,1.247474,1.2474739574 186627875,- 0.4258133721 25 E -7], +--R [0.94,1.238301,1.2383009959 262950556,- 0.4073704944 4 E -8], +--R [0.95,1.229384,1.2293839914 681003518,- 0.8531899648 15 E -8], +--R [0.96,1.2207157,1.2207156893 399160175,- 0.1066008398 25 E -7], +--R [0.97,1.2122891,1.2122891496 724233695,0.4967242336 95 E -7], +--R [0.98,1.2040977,1.2040977317 093965936,0.3170939659 36 E -7], +--R [0.99,1.1961351,1.1961350790 485799284,- 0.2095142007 16 E -7], +--R [1.0,1.1883951,1.1883951057 781212163,0.5778121216 3 E -8], +--R [1.01,1.180872,1.1808719834 468142375,- 0.1655318576 25 E -7], +--R [1.02,1.1735601,1.1735601288 11257282,0.2881125728 2 E -7], +--R [1.03,1.1664542,1.1664541923 074667313,- 0.7692533268 72 E -8], +--R [1.04,1.159549,1.1595490471 9853279,0.4719853279 E -7], +--R [1.05,1.1528398,1.1528397793 536064181,- 0.2064639358 19 E -7], +--R [1.06,1.1463217,1.1463216776 16894679,- 0.2238310532 1 E -7], +--R [1.07,1.1399902,1.1399902247 284454927,0.2472844549 27 E -7], +--R [1.08,1.1338411,1.1338410887 613485139,- 0.1123865148 61 E -7], +--R [1.09,1.1278701,1.1278701150 42590264,0.1504259026 4 E -7], +--R [1.1,1.1220733,1.1220733185 272000494,0.1852720004 94 E -7], +--R [1.11,1.1164469,1.1164468765 975278264,- 0.2340247217 36 E -7], +--R [1.12,1.1109871,1.1109871222 615233658,0.2226152336 58 E -7], +--R [1.13,1.1056905,1.1056905377 257534608,0.3772575346 08 E -7], +--R [1.14,1.1005537,1.1005537483 206146725,0.4832061467 25 E -7], +--R [1.15,1.0955735,1.0955735167 567859913,0.1675678599 13 E -7], +--R [1.16,1.0907467,1.0907467376 934304007,0.3769343040 07 E -7], +--R [1.17,1.0860704,1.0860704326 000071521,0.3260000715 21 E -7], +--R [1.18,1.0815417,1.0815417448 948071115,0.4489480711 15 E -7], +--R [1.19,1.0771579,1.0771579353 444804665,0.3534448046 65 E -7], +--R [1.2,1.0729164,1.0729163777 098972287,- 0.2229010277 13 E -7], +--R [1.21,1.0688146,1.0688145546 246734829,- 0.4537532651 71 E -7], +--R [1.22,1.0648501,1.0648500536 936167054,- 0.4630638329 46 E -7], +--R [1.23,1.0610206,1.0610205637 991976338,- 0.3620080236 62 E -7], +--R [1.24,1.0573239,1.0573238716 04949513,- 0.2839505048 7 E -7], +--R [1.25,1.0537579,1.0537578582 454329877,- 0.4175456701 23 E -7], +--R [1.26,1.0503205,1.0503204961 930909767,- 0.3806909023 3 E -8], +--R [1.27,1.0470098,1.0470098462 929566457,0.4629295664 57 E -7], +--R [1.28,1.0438241,1.0438240549 567728718,- 0.4504322712 82 E -7], +--R [1.29,1.0407614,1.0407613515 086368049,- 0.4849136319 51 E -7], +--R [1.3,1.03782,1.0378200456 748014427,0.4567480144 27 E -7], +--R [1.31,1.0349985,1.0349985252 107504451,0.2521075044 51 E -7], +--R [1.32,1.0322953,1.0322952536 591153897,- 0.4634088461 03 E -7], +--R [1.33,1.0297088,1.0297087682 324287489,- 0.3176757125 11 E -7], +--R [1.34,1.0272377,1.0272376778 151033218,- 0.2218489667 82 E -7], +--R [1.35,1.0248807,1.0248806610 794017372,- 0.3892059826 28 E -7], +--R [1.36,1.0226365,1.0226364647 10509886,- 0.3528949011 4 E -7], +--R [1.37,1.0205039,1.0205039017 361575009,0.1736157500 9 E -8], +--R [1.38,1.0184818,1.0184818499 565392157,0.4995653921 57 E -7], +--R [1.39,1.0165693,1.0165692504 705818114,- 0.4952941818 86 E -7], +--R [1.4,1.0147651,1.0147651062 948794009,0.6294879400 9 E -8], +--R [1.41,1.0130685,1.0130684810 718793105,- 0.1892812068 95 E -7], +--R [1.42,1.0114785,1.0114784978 641485933,- 0.2135851406 7 E -8], +--R [1.43,1.0099943,1.0099943380 317855887,0.3803178558 87 E -7], +--R [1.44,1.0086152,1.0086152401 902637594,0.4019026375 94 E -7], +--R [1.45,1.0073405,1.0073404992 46207189,- 0.753792811 E -9], +--R [1.46,1.0061695,1.0061694655 087995079,- 0.3449120049 21 E -7], +--R [1.47,1.0051015,1.0051015438 747215132,0.4387472151 32 E -7], +--R [1.48,1.0041362,1.0041361930 846981533,- 0.6915301846 7 E -8], +--R [1.49,1.0032729,1.0032729250 49913637,0.2504991363 7 E -7], +--R [1.5,1.0025113,1.0025113042 4672491,0.424672491 E -8], +--R [1.51,1.0018509,1.0018509471 78269319,0.4717826931 9 E -7], +--R [1.52,1.0012915,1.0012915219 017225962,0.2190172259 62 E -7], +--R [1.53,1.0008327,1.0008327476 201189712,0.4762011897 12 E -7], +--R [1.54,1.0004744,1.0004743943 377968613,- 0.5662203138 7 E -8], +--R [1.55,1.0002163,1.0002162825 786817653,- 0.1742131823 47 E -7], +--R [1.56,1.0000583,1.0000582831 667632601,- 0.1683323673 99 E -7], +--R [1.57,1.0000003,1.0000003170 68265912,0.1706826591 2 E -7], +--R [1.58,1.0000424,1.0000423552 951549942,- 0.4470484500 58 E -7], +--R [1.59,1.0001844,1.0001844188 697576625,0.1886975766 25 E -7], +--R [1.6,1.0004266,1.0004265788 504192126,- 0.2114958078 74 E -7]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp186-188 +\end{thebibliography} +\end{document} diff --git a/src/input/sincos.input.pamphlet b/src/input/sincos.input.pamphlet new file mode 100644 index 0000000..915ee4b --- /dev/null +++ b/src/input/sincos.input.pamphlet @@ -0,0 +1,696 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input sincos.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This compares Axiom's sincos function with the tables published in +Abramowitz and Stegun. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of sin(x), ranging from 0.00 to 1.60. The +second column is the reference value of sin from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp142-173 + +<<*>>= +)spool sincos.output +)set message test on +)set message auto off +)clear all +--S 1 of 2 +[[0.01,0.00999983333416666468254,sin(0.01),sin(0.01)-(0.00999983333416666468254)],_ +[0.02,0.01999866669333307936649,sin(0.02),sin(0.02)-(0.01999866669333307936649)],_ +[0.03,0.02999550020249566076853,sin(0.03),sin(0.03)-(0.02999550020249566076853)],_ +[0.04,0.03998933418663415945255,sin(0.04),sin(0.04)-(0.03998933418663415945255)],_ +[0.05,0.04997916927067832879487,sin(0.05),sin(0.05)-(0.04997916927067832879487)],_ +[0.06,0.05996400647944459919909,sin(0.06),sin(0.06)-(0.05996400647944459919909)],_ +[0.07,0.06994284733753276397655,sin(0.07),sin(0.07)-(0.06994284733753276397655)],_ +[0.08,0.07991469396917268730688,sin(0.08),sin(0.08)-(0.07991469396917268730688)],_ +[0.09,0.08987854919801104969125,sin(0.09),sin(0.09)-(0.08987854919801104969125)],_ +[0.10,0.09983341664682815230681,sin(0.10),sin(0.10)-(0.09983341664682815230681)],_ +[0.11,0.10977830083717480866495,sin(0.11),sin(0.11)-(0.10977830083717480866495)],_ +[0.12,0.11971220728891935996735,sin(0.12),sin(0.12)-(0.11971220728891935996735)],_ +[0.13,0.12963414261969485954121,sin(0.13),sin(0.13)-(0.12963414261969485954121)],_ +[0.14,0.13954311464423648171799,sin(0.14),sin(0.14)-(0.13954311464423648171799)],_ +[0.15,0.14943813247359922149773,sin(0.15),sin(0.15)-(0.14943813247359922149773)],_ +[0.16,0.15931820661424596331146,sin(0.16),sin(0.16)-(0.15931820661424596331146)],_ +[0.17,0.16918234906699601015762,sin(0.17),sin(0.17)-(0.16918234906699601015762)],_ +[0.18,0.17902957342582417834180,sin(0.18),sin(0.18)-(0.17902957342582417834180)],_ +[0.19,0.18885889497650057799285,sin(0.19),sin(0.19)-(0.18885889497650057799285)],_ +[0.20,0.19866933079506121545941,sin(0.20),sin(0.20)-(0.19866933079506121545941)],_ +[0.21,0.20845989984609957060871,sin(0.21),sin(0.21)-(0.20845989984609957060871)],_ +[0.22,0.21822962308086931995179,sin(0.22),sin(0.22)-(0.21822962308086931995179)],_ +[0.23,0.22797752353518839540462,sin(0.23),sin(0.23)-(0.22797752353518839540462)],_ +[0.24,0.23770262642713458836079,sin(0.24),sin(0.24)-(0.23770262642713458836079)],_ +[0.25,0.24740395925452292959685,sin(0.25),sin(0.25)-(0.24740395925452292959685)],_ +[0.26,0.25708055189215509735339,sin(0.26),sin(0.26)-(0.25708055189215509735339)],_ +[0.27,0.26673143668883112873229,sin(0.27),sin(0.27)-(0.26673143668883112873229)],_ +[0.28,0.27635564856411373331967,sin(0.28),sin(0.28)-(0.27635564856411373331967)],_ +[0.29,0.28595222510483553268394,sin(0.29),sin(0.29)-(0.28595222510483553268394)],_ +[0.30,0.29552020666133957510532,sin(0.30),sin(0.30)-(0.29552020666133957510532)],_ +[0.31,0.30505863644344350156564,sin(0.31),sin(0.31)-(0.30505863644344350156564)],_ +[0.32,0.31456656061611776666176,sin(0.32),sin(0.32)-(0.31456656061611776666176)],_ +[0.33,0.32404302839486834670020,sin(0.33),sin(0.33)-(0.32404302839486834670020)],_ +[0.34,0.33348709214081439678177,sin(0.34),sin(0.34)-(0.33348709214081439678177)],_ +[0.35,0.34289780745545134918963,sin(0.35),sin(0.35)-(0.34289780745545134918963)],_ +[0.36,0.35227423327508997684991,sin(0.36),sin(0.36)-(0.35227423327508997684991)],_ +[0.37,0.36161543196496197803729,sin(0.37),sin(0.37)-(0.36161543196496197803729)],_ +[0.38,0.37092046941298267184549,sin(0.38),sin(0.38)-(0.37092046941298267184549)],_ +[0.39,0.38018841512316142823118,sin(0.39),sin(0.39)-(0.38018841512316142823118)],_ +[0.40,0.38941834230865049166631,sin(0.40),sin(0.40)-(0.38941834230865049166631)],_ +[0.41,0.39860932798442289359380,sin(0.41),sin(0.41)-(0.39860932798442289359380)],_ +[0.42,0.40776045305957018597279,sin(0.42),sin(0.42)-(0.40776045305957018597279)],_ +[0.43,0.41687080242921076621692,sin(0.43),sin(0.43)-(0.41687080242921076621692)],_ +[0.44,0.42593946506599960276972,sin(0.44),sin(0.44)-(0.42593946506599960276972)],_ +[0.45,0.43496553411123021042084,sin(0.45),sin(0.45)-(0.43496553411123021042084)],_ +[0.46,0.44394810696551976524151,sin(0.46),sin(0.46)-(0.44394810696551976524151)],_ +[0.47,0.45288628537906829070327,sin(0.47),sin(0.47)-(0.45288628537906829070327)],_ +[0.48,0.46177917554148288913664,sin(0.48),sin(0.48)-(0.46177917554148288913664)],_ +[0.49,0.47062588817115803618136,sin(0.49),sin(0.49)-(0.47062588817115803618136)],_ +[0.50,0.47942553860420300027329,sin(0.50),sin(0.50)-(0.47942553860420300027329)],_ +[0.51,0.48817724688290749450013,sin(0.51),sin(0.51)-(0.48817724688290749450013)],_ +[0.52,0.49688013784373671433446,sin(0.52),sin(0.52)-(0.49688013784373671433446)],_ +[0.53,0.50553334120484696181366,sin(0.53),sin(0.53)-(0.50553334120484696181366)],_ +[0.54,0.51413599165311310467728,sin(0.54),sin(0.54)-(0.51413599165311310467728)],_ +[0.55,0.52268722893065916778838,sin(0.55),sin(0.55)-(0.52268722893065916778838)],_ +[0.56,0.53118619792088340385187,sin(0.56),sin(0.56)-(0.53118619792088340385187)],_ +[0.57,0.53963204873396924099446,sin(0.57),sin(0.57)-(0.53963204873396924099446)],_ +[0.58,0.54802393679187355618270,sin(0.58),sin(0.58)-(0.54802393679187355618270)],_ +[0.59,0.55636102291278377572254,sin(0.59),sin(0.59)-(0.55636102291278377572254)],_ +[0.60,0.56464247339503535720095,sin(0.60),sin(0.60)-(0.56464247339503535720095)],_ +[0.61,0.57286746010048126119098,sin(0.61),sin(0.61)-(0.57286746010048126119098)],_ +[0.62,0.58103516053730507584296,sin(0.62),sin(0.62)-(0.58103516053730507584296)],_ +[0.63,0.58914475794226951311811,sin(0.63),sin(0.63)-(0.58914475794226951311811)],_ +[0.64,0.59719544136239205188355,sin(0.64),sin(0.64)-(0.59719544136239205188355)],_ +[0.65,0.60518640573603956037252,sin(0.65),sin(0.65)-(0.60518640573603956037252)],_ +[0.66,0.61311685197343378861515,sin(0.66),sin(0.66)-(0.61311685197343378861515)],_ +[0.67,0.62098598703655968035744,sin(0.67),sin(0.67)-(0.62098598703655968035744)],_ +[0.68,0.62879302401846851370418,sin(0.68),sin(0.68)-(0.62879302401846851370418)],_ +[0.69,0.63653718222196794023743,sin(0.69),sin(0.69)-(0.63653718222196794023743)],_ +[0.70,0.64421768723769105367261,sin(0.70),sin(0.70)-(0.64421768723769105367261)],_ +[0.71,0.65183377102153668121013,sin(0.71),sin(0.71)-(0.65183377102153668121013)],_ +[0.72,0.65938467197147315361800,sin(0.72),sin(0.72)-(0.65938467197147315361800)],_ +[0.73,0.66686963500369787373259,sin(0.73),sin(0.73)-(0.66686963500369787373259)],_ +[0.74,0.67428791162814506748388,sin(0.74),sin(0.74)-(0.67428791162814506748388)],_ +[0.75,0.68163876002333416673324,sin(0.75),sin(0.75)-(0.68163876002333416673324)],_ +[0.76,0.68892144511055133914776,sin(0.76),sin(0.76)-(0.68892144511055133914776)],_ +[0.77,0.69613523862735674701988,sin(0.77),sin(0.77)-(0.69613523862735674701988)],_ +[0.78,0.70327941920041018436790,sin(0.78),sin(0.78)-(0.70327941920041018436790)],_ +[0.79,0.71035327241760780981403,sin(0.79),sin(0.79)-(0.71035327241760780981403)],_ +[0.80,0.71735609089952276162718,sin(0.80),sin(0.80)-(0.71735609089952276162718)],_ +[0.81,0.72428717437014251092818,sin(0.81),sin(0.81)-(0.72428717437014251092818)],_ +[0.82,0.73114582972689587938131,sin(0.82),sin(0.82)-(0.73114582972689587938131)],_ +[0.83,0.73793137110996271872858,sin(0.83),sin(0.83)-(0.73793137110996271872858)],_ +[0.84,0.74464311997085932125657,sin(0.84),sin(0.84)-(0.74464311997085932125657)],_ +[0.85,0.75128040514029270271207,sin(0.85),sin(0.85)-(0.75128040514029270271207)],_ +[0.86,0.75784256289527697229459,sin(0.86),sin(0.86)-(0.75784256289527697229459)],_ +[0.87,0.76432893702550507814480,sin(0.87),sin(0.87)-(0.76432893702550507814480)],_ +[0.88,0.77073887889896929120965,sin(0.88),sin(0.88)-(0.77073887889896929120965)],_ +[0.89,0.77707174752682386549033,sin(0.89),sin(0.89)-(0.77707174752682386549033)],_ +[0.90,0.78332690962748338846138,sin(0.90),sin(0.90)-(0.78332690962748338846138)],_ +[0.91,0.78950373968995041187896,sin(0.91),sin(0.91)-(0.78950373968995041187896)],_ +[0.92,0.79560162003636603026828,sin(0.92),sin(0.92)-(0.79560162003636603026828)],_ +[0.93,0.80161994088377715208432,sin(0.93),sin(0.93)-(0.80161994088377715208432)],_ +[0.94,0.80755810040511428687022,sin(0.94),sin(0.94)-(0.80755810040511428687022)],_ +[0.95,0.81341550478937375068542,sin(0.95),sin(0.95)-(0.81341550478937375068542)],_ +[0.96,0.81919156830099827163322,sin(0.96),sin(0.96)-(0.81919156830099827163322)],_ +[0.97,0.82488571333845005747662,sin(0.97),sin(0.97)-(0.82488571333845005747662)],_ +[0.98,0.83049737049197046808453,sin(0.98),sin(0.98)-(0.83049737049197046808453)],_ 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[1.11,0.8956986856 8004762924,0.8956986856 8004762924,0.0], +--R [1.12,0.9001004421 7650499712,0.9001004421 7650499712,0.0], +--R [1.13,0.9044121893 7882591604,0.9044121893 7882591604,0.0], +--R [1.14,0.9086334961 1588326459,0.9086334961 1588326459,0.0], +--R [1.15,0.9127639402 6052108094,0.9127639402 6052108094,0.0], +--R [1.16,0.9168031087 7176692662,0.9168031087 7176692662,- 0.3 E -20], +--R [1.17,0.9207505977 3613563957,0.9207505977 3613563958,0.3 E -20], +--R [1.18,0.9246060124 0802034611,0.9246060124 0802034611,0.0], +--R [1.19,0.9283689672 491666926,0.9283689672 491666926,0.0], +--R [1.2,0.9320390859 6722634967,0.9320390859 6722634967,0.3 E -20], +--R [1.21,0.9356160015 5338593342,0.9356160015 5338593342,0.0], +--R [1.22,0.9390993563 1906758094,0.9390993563 1906758094,0.0], +--R [1.23,0.9424888019 3169751002,0.9424888019 3169751002,0.0], +--R [1.24,0.9457839994 4953898629,0.9457839994 4953898629,0.0], +--R [1.25,0.9489846193 5558621435,0.9489846193 5558621435,0.0], +--R [1.26,0.9520903415 9051576386,0.9520903415 9051576386,0.0], +--R [1.27,0.9551008555 8469223509,0.9551008555 8469223509,0.0], +--R [1.28,0.9580158602 892249637,0.9580158602 892249637,0.0], +--R [1.29,0.9608350642 0607265891,0.9608350642 0607265891,0.0], +--R [1.3,0.9635581854 171929647,0.9635581854 171929647,- 0.3 E -20], +--R [1.31,0.9661849516 1273402917,0.9661849516 1273402917,0.0], +--R [1.32,0.9687151001 1826526273,0.9687151001 1826526273,0.0], +--R [1.33,0.9711483779 2104456234,0.9711483779 2104456234,0.0], +--R [1.34,0.9734845416 9531937479,0.9734845416 9531937479,0.0], +--R [1.35,0.9757233578 2665906926,0.9757233578 2665906926,0.0], +--R [1.36,0.9778646024 3531618568,0.9778646024 3531618568,0.0], +--R [1.37,0.9799080613 9861422289,0.9799080613 9861422289,0.0], +--R [1.38,0.9818535303 7235972788,0.9818535303 7235972788,0.0], +--R [1.39,0.9837008148 1127654484,0.9837008148 1127654484,0.0], +--R [1.4,0.9854497299 8846018066,0.9854497299 8846018066,0.0], +--R [1.41,0.9871001010 1385034143,0.9871001010 1385034143,0.0], +--R [1.42,0.9886517628 5171979274,0.9886517628 5171979274,0.0], +--R [1.43,0.9901045603 3717779486,0.9901045603 3717779486,0.0], +--R [1.44,0.9914583481 9168646253,0.9914583481 9168646253,0.0], +--R [1.45,0.9927129910 3758849767,0.9927129910 3758849767,0.0], +--R [1.46,0.9938683634 1164484229,0.9938683634 1164484229,0.0], +--R [1.47,0.9949243497 7758089786,0.9949243497 7758089786,0.0], +--R [1.48,0.9958808445 3764005648,0.9958808445 3764005648,0.0], +--R [1.49,0.9967377520 4314338855,0.9967377520 4314338855,0.0], +--R [1.5,0.9974949866 0405443094,0.9974949866 0405443094,0.0], +--R [1.51,0.9981524724 9754811924,0.9981524724 9754811924,0.0], +--R [1.52,0.9987101439 7558300717,0.9987101439 7558300717,0.0], +--R [1.53,0.9991679452 7147601592,0.9991679452 7147601592,0.0], +--R [1.54,0.9995258306 0547905601,0.9995258306 0547905601,0.0], +--R [1.55,0.9997837641 893569639,0.9997837641 893569639,0.0], +--R [1.56,0.9999417202 2996629574,0.9999417202 2996629574,0.0], +--R [1.57,0.9999996829 3183462021,0.9999996829 3183462021,0.0], +--R [1.58,0.9999576464 9874005255,0.9999576464 9874005255,0.0], +--R [1.59,0.9998156151 3429087198,0.9998156151 3429087198,0.0], +--R [1.6,0.9995736030 4150516434,0.9995736030 4150516434,0.0]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of cos(x), ranging from 0.00 to 1.60. The +second column is the reference value of sin from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp142-173 + +<<*>>= +--S 2 of 2 +[[0.01,0.99995000041666527778026,cos(0.01),cos(0.01)-(0.99995000041666527778026)],_ +[0.02,0.99980000666657777841270,cos(0.02),cos(0.02)-(0.99980000666657777841270)],_ +[0.03,0.99955003374898751627216,cos(0.03),cos(0.03)-(0.99955003374898751627216)],_ +[0.04,0.99920010666097794031457,cos(0.04),cos(0.04)-(0.99920010666097794031457)],_ +[0.05,0.99875026039496624656287,cos(0.05),cos(0.05)-(0.99875026039496624656287)],_ +[0.06,0.99820053993520416554766,cos(0.06),cos(0.06)-(0.99820053993520416554766)],_ +[0.07,0.99755100025327957462091,cos(0.07),cos(0.07)-(0.99755100025327957462091)],_ +[0.08,0.99680170630261938497771,cos(0.08),cos(0.08)-(0.99680170630261938497771)],_ +[0.09,0.99595273301199425309284,cos(0.09),cos(0.09)-(0.99595273301199425309284)],_ +[0.10,0.99500416527802576609556,cos(0.10),cos(0.10)-(0.99500416527802576609556)],_ +[0.11,0.99395609795669685035784,cos(0.11),cos(0.11)-(0.99395609795669685035784)],_ +[0.12,0.99280863585386625224810,cos(0.12),cos(0.12)-(0.99280863585386625224810)],_ +[0.13,0.99156189371478803959451,cos(0.13),cos(0.13)-(0.99156189371478803959451)],_ +[0.14,0.99021599621263717189895,cos(0.14),cos(0.14)-(0.99021599621263717189895)],_ +[0.15,0.98877107793604228673498,cos(0.15),cos(0.15)-(0.98877107793604228673498)],_ +[0.16,0.98722728337562694904095,cos(0.16),cos(0.16)-(0.98722728337562694904095)],_ +[0.17,0.98558476690956070917193,cos(0.17),cos(0.17)-(0.98558476690956070917193)],_ +[0.18,0.98384369278812141459272,cos(0.18),cos(0.18)-(0.98384369278812141459272)],_ +[0.19,0.98200423511727031896788,cos(0.19),cos(0.19)-(0.98200423511727031896788)],_ +[0.20,0.98006657784124163112420,cos(0.20),cos(0.20)-(0.98006657784124163112420)],_ +[0.21,0.97803091472414824491614,cos(0.21),cos(0.21)-(0.97803091472414824491614)],_ +[0.22,0.97589744933060548940602,cos(0.22),cos(0.22)-(0.97589744933060548940602)],_ +[0.23,0.97366639500537483696773,cos(0.23),cos(0.23)-(0.97366639500537483696773)],_ +[0.24,0.97133797485202960492618,cos(0.24),cos(0.24)-(0.97133797485202960492618)],_ +[0.25,0.96891242171064478414459,cos(0.25),cos(0.25)-(0.96891242171064478414459)],_ +[0.26,0.96638997813451322555822,cos(0.26),cos(0.26)-(0.96638997813451322555822)],_ +[0.27,0.96377089636589051301623,cos(0.27),cos(0.27)-(0.96377089636589051301623)],_ +[0.28,0.96105543831077094792459,cos(0.28),cos(0.28)-(0.96105543831077094792459)],_ +[0.29,0.95824387551269716807013,cos(0.29),cos(0.29)-(0.95824387551269716807013)],_ +[0.30,0.95533648912560601964231,cos(0.30),cos(0.30)-(0.95533648912560601964231)],_ +[0.31,0.95233356988571339784281,cos(0.31),cos(0.31)-(0.95233356988571339784281)],_ +[0.32,0.94923541808244086757531,cos(0.32),cos(0.32)-(0.94923541808244086757531)],_ +[0.33,0.94604234352838697152941,cos(0.33),cos(0.33)-(0.94604234352838697152941)],_ +[0.34,0.94275466552834622850264,cos(0.34),cos(0.34)-(0.94275466552834622850264)],_ +[0.35,0.93937271284737892003503,cos(0.35),cos(0.35)-(0.93937271284737892003503)],_ +[0.36,0.93589682367793485835091,cos(0.36),cos(0.36)-(0.93589682367793485835091)],_ +[0.37,0.93232734560603442320381,cos(0.37),cos(0.37)-(0.93232734560603442320381)],_ +[0.38,0.92866463557651024949253,cos(0.38),cos(0.38)-(0.92866463557651024949253)],_ +[0.39,0.92490905985731304145068,cos(0.39),cos(0.39)-(0.92490905985731304145068)],_ +[0.40,0.92106099400288508279853,cos(0.40),cos(0.40)-(0.92106099400288508279853)],_ +[0.41,0.91712082281660510547564,cos(0.41),cos(0.41)-(0.91712082281660510547564)],_ +[0.42,0.91308894031230827243609,cos(0.42),cos(0.42)-(0.91308894031230827243609)],_ +[0.43,0.90896574967488512247591,cos(0.43),cos(0.43)-(0.90896574967488512247591)],_ +[0.44,0.90475166321996341716554,cos(0.44),cos(0.44)-(0.90475166321996341716554)],_ +[0.45,0.90044710235267692166884,cos(0.45),cos(0.45)-(0.90044710235267692166884)],_ +[0.46,0.89605249752552524253639,cos(0.46),cos(0.46)-(0.89605249752552524253639)],_ +[0.47,0.89156828819532893645402,cos(0.47),cos(0.47)-(0.89156828819532893645402)],_ +[0.48,0.88699492277928419439995,cos(0.48),cos(0.48)-(0.88699492277928419439995)],_ +[0.49,0.88233285861012149570547,cos(0.49),cos(0.49)-(0.88233285861012149570547)],_ +[0.50,0.87758256189037271611628,cos(0.50),cos(0.50)-(0.87758256189037271611628)],_ +[0.51,0.87274450764575126310581,cos(0.51),cos(0.51)-(0.87274450764575126310581)],_ +[0.52,0.86781917967764990038785,cos(0.52),cos(0.52)-(0.86781917967764990038785)],_ +[0.53,0.86280707051476101180670,cos(0.53),cos(0.53)-(0.86280707051476101180670)],_ +[0.54,0.85770868136382414253797,cos(0.54),cos(0.54)-(0.85770868136382414253797)],_ +[0.55,0.85252452205950574280498,cos(0.55),cos(0.55)-(0.85252452205950574280498)],_ +[0.56,0.84725511101341612609452,cos(0.56),cos(0.56)-(0.84725511101341612609452)],_ +[0.57,0.84190097516226874013376,cos(0.57),cos(0.57)-(0.84190097516226874013376)],_ +[0.58,0.83646264991518693465789,cos(0.58),cos(0.58)-(0.83646264991518693465789)],_ +[0.59,0.83094067910016349524800,cos(0.59),cos(0.59)-(0.83094067910016349524800)],_ +[0.60,0.82533561490967829724095,cos(0.60),cos(0.60)-(0.82533561490967829724095)],_ +[0.61,0.81964801784547951790075,cos(0.61),cos(0.61)-(0.81964801784547951790075)],_ +[0.62,0.81387845666253392868400,cos(0.62),cos(0.62)-(0.81387845666253392868400)],_ +[0.63,0.80802750831215187252371,cos(0.63),cos(0.63)-(0.80802750831215187252371)],_ +[0.64,0.80209575788429261358611,cos(0.64),cos(0.64)-(0.80209575788429261358611)],_ +[0.65,0.79608379854905582891760,cos(0.65),cos(0.65)-(0.79608379854905582891760)],_ +[0.66,0.78999223149736509278382,cos(0.66),cos(0.66)-(0.78999223149736509278382)],_ +[0.67,0.78382166588084928530294,cos(0.67),cos(0.67)-(0.78382166588084928530294)],_ +[0.68,0.77757271875092793718239,cos(0.68),cos(0.68)-(0.77757271875092793718239)],_ +[0.69,0.77124601499710660197354,cos(0.69),cos(0.69)-(0.77124601499710660197354)],_ +[0.70,0.76484218728448842625586,cos(0.70),cos(0.70)-(0.76484218728448842625586)],_ +[0.71,0.75836187599050816654146,cos(0.71),cos(0.71)-(0.75836187599050816654146)],_ +[0.72,0.75180572914089497944549,cos(0.72),cos(0.72)-(0.75180572914089497944549)],_ +[0.73,0.74517440234487038879013,cos(0.73),cos(0.73)-(0.74517440234487038879013)],_ +[0.74,0.73846855872958790979142,cos(0.74),cos(0.74)-(0.73846855872958790979142)],_ +[0.75,0.73168886887382088631184,cos(0.75),cos(0.75)-(0.73168886887382088631184)],_ +[0.76,0.72483601074090517233969,cos(0.76),cos(0.76)-(0.72483601074090517233969)],_ +[0.77,0.71791066961094336337129,cos(0.77),cos(0.77)-(0.71791066961094336337129)],_ +[0.78,0.71091353801227735721626,cos(0.78),cos(0.78)-(0.71091353801227735721626)],_ +[0.79,0.70384531565223609691278,cos(0.79),cos(0.79)-(0.70384531565223609691278)],_ +[0.80,0.69670670934716542092075,cos(0.80),cos(0.80)-(0.69670670934716542092075)],_ +[0.81,0.68949843295174701754964,cos(0.81),cos(0.81)-(0.68949843295174701754964)],_ +[0.82,0.68222120728761355166656,cos(0.82),cos(0.82)-(0.68222120728761355166656)],_ +[0.83,0.67487576007126710211246,cos(0.83),cos(0.83)-(0.67487576007126710211246)],_ +[0.84,0.66746282584130811792267,cos(0.84),cos(0.84)-(0.66746282584130811792267)],_ +[0.85,0.65998314588498217039542,cos(0.85),cos(0.85)-(0.65998314588498217039542)],_ +[0.86,0.65243746816405184627203,cos(0.86),cos(0.86)-(0.65243746816405184627203)],_ +[0.87,0.64482654724000119477766,cos(0.87),cos(0.87)-(0.64482654724000119477766)],_ +[0.88,0.63715114419858020801550,cos(0.88),cos(0.88)-(0.63715114419858020801550)],_ 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[1.28,0.2867152096 3195551278,0.2867152096 3195551278,- 0.2 E -20], +--R [1.29,0.2771208750 5655764139,0.2771208750 5655764139,0.0], +--R [1.3,0.2674988286 24587407,0.2674988286 24587407,0.2 E -20], +--R [1.31,0.2578500325 3266966134,0.2578500325 3266966134,- 0.3 E -20], +--R [1.32,0.2481754516 5237295957,0.2481754516 5237295957,0.0], +--R [1.33,0.2384760534 3372320752,0.2384760534 3372320752,0.8 E -21], +--R [1.34,0.2287528078 0845946523,0.2287528078 0845946523,- 0.3 E -20], +--R [1.35,0.2190066870 9304158142,0.2190066870 9304158142,- 0.2 E -20], +--R [1.36,0.2092386658 9141935768,0.2092386658 9141935768,0.0], +--R [1.37,0.1994497209 9757296569,0.1994497209 9757296569,0.2 E -20], +--R [1.38,0.1896408312 9783436321,0.1896408312 9783436321,- 0.3 E -20], +--R [1.39,0.1798129776 729994766,0.1798129776 729994766,- 0.8 E -21], +--R [1.4,0.1699671429 0024093862,0.1699671429 0024093862,0.8 E -21], +--R [1.41,0.1601043115 5483119016,0.1601043115 5483119017,0.3 E -20], +--R [1.42,0.1502254699 1168577349,0.1502254699 1168577349,- 0.2 E -20], +--R [1.43,0.1403316058 4673666253,0.1403316058 4673666253,0.0], +--R [1.44,0.1304237087 3814549298,0.1304237087 3814549298,0.2 E -20], +--R [1.45,0.1205027693 6736657053,0.1205027693 6736657053,- 0.3 E -20], +--R [1.46,0.1105697798 2006955117,0.1105697798 2006955117,- 0.8 E -21], +--R [1.47,0.1006257333 8693170091,0.1006257333 8693170091,0.8 E -21], +--R [1.48,0.0906716244 6430965577 6,0.0906716244 6430965577 9,0.3 E -20], +--R [1.49,0.0807084484 5480061486 8,0.0807084484 5480061486 6,- 0.2 E -20], +--R [1.5,0.0707372016 6770291008 8,0.0707372016 6770291008 8,0.0], +--R [1.51,0.0607588812 1938590658 2,0.0607588812 1938590658 3,0.2 E -20], +--R [1.52,0.0507744849 3357919672 6,0.0507744849 3357919672 3,- 0.3 E -20], +--R [1.53,0.0407850112 4159105868 9,0.0407850112 4159105868 8,- 0.1 E -20], +--R [1.54,0.0307914590 8246615762 2,0.0307914590 8246615762 3,0.8 E -21], +--R [1.55,0.0207948278 0309247364 4,0.0207948278 0309247364 7,0.3 E -20], +--R [1.56,0.0107961170 5826744582 4,0.0107961170 5826744582 2,- 0.2 E -20], +--R [1.57,0.0007963267 1073332548 541,0.0007963267 1073332548 514,- 0.3 E -21], +--R [1.58,- 0.0092035432 6880826480 54,- 0.0092035432 6880826480 38,0.2 E -20], +--R [1.59,- 0.0192024929 0169256809 5,- 0.0192024929 0169256809 8,- 0.3 E -20], +--R [1.6,- 0.0291995223 0128872620 6,- 0.0291995223 0128872620 7,- 0.1 E -20]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} Abramowitz and Stegun,``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp142-173 +\end{thebibliography} +\end{document} + diff --git a/src/input/sinhcosh.input.pamphlet b/src/input/sinhcosh.input.pamphlet new file mode 100644 index 0000000..aa23267 --- /dev/null +++ b/src/input/sinhcosh.input.pamphlet @@ -0,0 +1,861 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input sinhcosh.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is a set of tests for the sinh and cosh functions. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of sinh, ranging from 0.00 to 2.00. The +second column is the reference value of sinh from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp213-216 + +<<*>>= +)spool sinhcosh.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.00,0.000000000,sinh(0.00),sinh(0.00)-0.000000000],_ +[0.01,0.010000167,sinh(0.01),sinh(0.01)-0.010000167],_ +[0.02,0.020001333,sinh(0.02),sinh(0.02)-0.020001333],_ +[0.03,0.030004500,sinh(0.03),sinh(0.03)-0.030004500],_ +[0.04,0.040010668,sinh(0.04),sinh(0.04)-0.040010668],_ +[0.05,0.050020836,sinh(0.05),sinh(0.05)-0.050020836],_ +[0.06,0.060036006,sinh(0.06),sinh(0.06)-0.060036006],_ +[0.07,0.070057181,sinh(0.07),sinh(0.07)-0.070057181],_ +[0.08,0.080085361,sinh(0.08),sinh(0.08)-0.080085361],_ +[0.09,0.090121549,sinh(0.09),sinh(0.09)-0.090121549],_ +[0.10,0.100166750,sinh(0.10),sinh(0.10)-0.100166750],_ +[0.11,0.110221968,sinh(0.11),sinh(0.11)-0.110221968],_ +[0.12,0.120288207,sinh(0.12),sinh(0.12)-0.120288207],_ +[0.13,0.130366476,sinh(0.13),sinh(0.13)-0.130366476],_ +[0.14,0.140457782,sinh(0.14),sinh(0.14)-0.140457782],_ +[0.15,0.150563133,sinh(0.15),sinh(0.15)-0.150563133],_ +[0.16,0.160683541,sinh(0.16),sinh(0.16)-0.160683541],_ +[0.17,0.170820017,sinh(0.17),sinh(0.17)-0.170820017],_ +[0.18,0.180973576,sinh(0.18),sinh(0.18)-0.180973576],_ +[0.19,0.191145232,sinh(0.19),sinh(0.19)-0.191145232],_ +[0.20,0.201336003,sinh(0.20),sinh(0.20)-0.201336003],_ +[0.21,0.211546907,sinh(0.21),sinh(0.21)-0.211546907],_ +[0.22,0.221778966,sinh(0.22),sinh(0.22)-0.221778966],_ +[0.23,0.232033204,sinh(0.23),sinh(0.23)-0.232033204],_ +[0.24,0.242310645,sinh(0.24),sinh(0.24)-0.242310645],_ +[0.25,0.252612317,sinh(0.25),sinh(0.25)-0.252612317],_ +[0.26,0.262939250,sinh(0.26),sinh(0.26)-0.262939250],_ +[0.27,0.273292478,sinh(0.27),sinh(0.27)-0.273292478],_ +[0.28,0.283673035,sinh(0.28),sinh(0.28)-0.283673035],_ +[0.29,0.294081960,sinh(0.29),sinh(0.29)-0.294081960],_ +[0.30,0.304520293,sinh(0.30),sinh(0.30)-0.304520293],_ +[0.31,0.314989079,sinh(0.31),sinh(0.31)-0.314989079],_ +[0.32,0.325489364,sinh(0.32),sinh(0.32)-0.325489364],_ +[0.33,0.336022198,sinh(0.33),sinh(0.33)-0.336022198],_ +[0.34,0.346588634,sinh(0.34),sinh(0.34)-0.346588634],_ +[0.35,0.357189729,sinh(0.35),sinh(0.35)-0.357189729],_ +[0.36,0.367826544,sinh(0.36),sinh(0.36)-0.367826544],_ +[0.37,0.378500142,sinh(0.37),sinh(0.37)-0.378500142],_ +[0.38,0.389211590,sinh(0.38),sinh(0.38)-0.389211590],_ +[0.39,0.399961960,sinh(0.39),sinh(0.39)-0.399961960],_ +[0.40,0.410752326,sinh(0.40),sinh(0.40)-0.410752326],_ +[0.41,0.421583767,sinh(0.41),sinh(0.41)-0.421583767],_ +[0.42,0.432457368,sinh(0.42),sinh(0.42)-0.432457368],_ +[0.43,0.443374214,sinh(0.43),sinh(0.43)-0.443374214],_ +[0.44,0.454335399,sinh(0.44),sinh(0.44)-0.454335399],_ +[0.45,0.465342017,sinh(0.45),sinh(0.45)-0.465342017],_ +[0.46,0.476395170,sinh(0.46),sinh(0.46)-0.476395170],_ +[0.47,0.487495962,sinh(0.47),sinh(0.47)-0.487495962],_ +[0.48,0.498645505,sinh(0.48),sinh(0.48)-0.498645505],_ +[0.49,0.509844913,sinh(0.49),sinh(0.49)-0.509844913],_ +[0.50,0.521095305,sinh(0.50),sinh(0.50)-0.521095305],_ +[0.51,0.532397808,sinh(0.51),sinh(0.51)-0.532397808],_ +[0.52,0.543753551,sinh(0.52),sinh(0.52)-0.543753551],_ +[0.53,0.555163669,sinh(0.53),sinh(0.53)-0.555163669],_ +[0.54,0.566629305,sinh(0.54),sinh(0.54)-0.566629305],_ +[0.55,0.578151604,sinh(0.55),sinh(0.55)-0.578151604],_ +[0.56,0.589731718,sinh(0.56),sinh(0.56)-0.589731718],_ +[0.57,0.601370806,sinh(0.57),sinh(0.57)-0.601370806],_ +[0.58,0.613070032,sinh(0.58),sinh(0.58)-0.613070032],_ +[0.59,0.624830565,sinh(0.59),sinh(0.59)-0.624830565],_ +[0.60,0.636653582,sinh(0.60),sinh(0.60)-0.636653582],_ +[0.61,0.648540265,sinh(0.61),sinh(0.61)-0.648540265],_ +[0.62,0.660491802,sinh(0.62),sinh(0.62)-0.660491802],_ +[0.63,0.672509389,sinh(0.63),sinh(0.63)-0.672509389],_ +[0.64,0.684594228,sinh(0.64),sinh(0.64)-0.684594228],_ +[0.65,0.696747526,sinh(0.65),sinh(0.65)-0.696747526],_ +[0.66,0.708970500,sinh(0.66),sinh(0.66)-0.708970500],_ +[0.67,0.721264371,sinh(0.67),sinh(0.67)-0.721264371],_ +[0.68,0.733630370,sinh(0.68),sinh(0.68)-0.733630370],_ +[0.69,0.746069732,sinh(0.69),sinh(0.69)-0.746069732],_ +[0.70,0.758583702,sinh(0.70),sinh(0.70)-0.758583702],_ +[0.71,0.771173531,sinh(0.71),sinh(0.71)-0.771173531],_ +[0.72,0.783840477,sinh(0.72),sinh(0.72)-0.783840477],_ +[0.73,0.796585809,sinh(0.73),sinh(0.73)-0.796585809],_ +[0.74,0.809410799,sinh(0.74),sinh(0.74)-0.809410799],_ +[0.75,0.822316732,sinh(0.75),sinh(0.75)-0.822316732],_ +[0.76,0.835304897,sinh(0.76),sinh(0.76)-0.835304897],_ +[0.77,0.848376593,sinh(0.77),sinh(0.77)-0.848376593],_ +[0.78,0.861533127,sinh(0.78),sinh(0.78)-0.861533127],_ +[0.79,0.874775815,sinh(0.79),sinh(0.79)-0.874775815],_ +[0.80,0.888105982,sinh(0.80),sinh(0.80)-0.888105982],_ +[0.81,0.901524960,sinh(0.81),sinh(0.81)-0.901524960],_ +[0.82,0.915034092,sinh(0.82),sinh(0.82)-0.915034092],_ +[0.83,0.928634727,sinh(0.83),sinh(0.83)-0.928634727],_ +[0.84,0.942328227,sinh(0.84),sinh(0.84)-0.942328227],_ +[0.85,0.956115960,sinh(0.85),sinh(0.85)-0.956115960],_ +[0.86,0.969999306,sinh(0.86),sinh(0.86)-0.969999306],_ +[0.87,0.983979652,sinh(0.87),sinh(0.87)-0.983979652],_ +[0.88,0.998058397,sinh(0.88),sinh(0.88)-0.998058397],_ +[0.89,1.012236949,sinh(0.89),sinh(0.89)-1.012236949],_ +[0.90,1.026516726,sinh(0.90),sinh(0.90)-1.026516726],_ +[0.91,1.040899155,sinh(0.91),sinh(0.91)-1.040899155],_ +[0.92,1.055385674,sinh(0.92),sinh(0.92)-1.055385674],_ +[0.93,1.069977734,sinh(0.93),sinh(0.93)-1.069977734],_ +[0.94,1.084676791,sinh(0.94),sinh(0.94)-1.084676791],_ +[0.95,1.099484318,sinh(0.95),sinh(0.95)-1.099484318],_ +[0.96,1.114401794,sinh(0.96),sinh(0.96)-1.114401794],_ +[0.97,1.129430711,sinh(0.97),sinh(0.97)-1.129430711],_ +[0.98,1.144572572,sinh(0.98),sinh(0.98)-1.144572572],_ +[0.99,1.159828891,sinh(0.99),sinh(0.99)-1.159828891],_ +[1.00,1.175201194,sinh(1.00),sinh(1.00)-1.175201194],_ +[1.01,1.190691018,sinh(1.01),sinh(1.01)-1.190691018],_ +[1.02,1.206299912,sinh(1.02),sinh(1.02)-1.206299912],_ +[1.03,1.222029437,sinh(1.03),sinh(1.03)-1.222029437],_ +[1.04,1.237881166,sinh(1.04),sinh(1.04)-1.237881166],_ +[1.05,1.253856684,sinh(1.05),sinh(1.05)-1.253856684],_ +[1.06,1.269957589,sinh(1.06),sinh(1.06)-1.269957589],_ +[1.07,1.286185491,sinh(1.07),sinh(1.07)-1.286185491],_ +[1.08,1.302542013,sinh(1.08),sinh(1.08)-1.302542013],_ +[1.09,1.319028789,sinh(1.09),sinh(1.09)-1.319028789],_ +[1.10,1.335647470,sinh(1.10),sinh(1.10)-1.335647470],_ +[1.11,1.352399717,sinh(1.11),sinh(1.11)-1.352399717],_ +[1.12,1.369287204,sinh(1.12),sinh(1.12)-1.369287204],_ +[1.13,1.386311622,sinh(1.13),sinh(1.13)-1.386311622],_ +[1.14,1.403474672,sinh(1.14),sinh(1.14)-1.403474672],_ +[1.15,1.420778070,sinh(1.15),sinh(1.15)-1.420778070],_ +[1.16,1.438223548,sinh(1.16),sinh(1.16)-1.438223548],_ +[1.17,1.455812849,sinh(1.17),sinh(1.17)-1.455812849],_ +[1.18,1.473547732,sinh(1.18),sinh(1.18)-1.473547732],_ +[1.19,1.491429972,sinh(1.19),sinh(1.19)-1.491429972],_ +[1.20,1.509461355,sinh(1.20),sinh(1.20)-1.509461355],_ +[1.21,1.527643687,sinh(1.21),sinh(1.21)-1.527643687],_ +[1.22,1.545978783,sinh(1.22),sinh(1.22)-1.545978783],_ +[1.23,1.564468479,sinh(1.23),sinh(1.23)-1.564468479],_ +[1.24,1.583114623,sinh(1.24),sinh(1.24)-1.583114623],_ +[1.25,1.601919080,sinh(1.25),sinh(1.25)-1.601919080],_ +[1.26,1.620883730,sinh(1.26),sinh(1.26)-1.620883730],_ +[1.27,1.640010470,sinh(1.27),sinh(1.27)-1.640010470],_ +[1.28,1.659301213,sinh(1.28),sinh(1.28)-1.659301213],_ +[1.29,1.678757886,sinh(1.29),sinh(1.29)-1.678757886],_ +[1.30,1.698382437,sinh(1.30),sinh(1.30)-1.698382437],_ +[1.31,1.718176828,sinh(1.31),sinh(1.31)-1.718176828],_ +[1.32,1.738143038,sinh(1.32),sinh(1.32)-1.738143038],_ +[1.33,1.758283063,sinh(1.33),sinh(1.33)-1.758283063],_ +[1.34,1.778598918,sinh(1.34),sinh(1.34)-1.778598918],_ +[1.35,1.799092635,sinh(1.35),sinh(1.35)-1.799092635],_ +[1.36,1.819766262,sinh(1.36),sinh(1.36)-1.819766262],_ +[1.37,1.840621868,sinh(1.37),sinh(1.37)-1.840621868],_ +[1.38,1.861661537,sinh(1.38),sinh(1.38)-1.861661537],_ +[1.39,1.882887374,sinh(1.39),sinh(1.39)-1.882887374],_ +[1.40,1.904301501,sinh(1.40),sinh(1.40)-1.904301501],_ +[1.41,1.925906060,sinh(1.41),sinh(1.41)-1.925906060],_ +[1.42,1.947703212,sinh(1.42),sinh(1.42)-1.947703212],_ +[1.43,1.969695135,sinh(1.43),sinh(1.43)-1.969695135],_ +[1.44,1.991884029,sinh(1.44),sinh(1.44)-1.991884029],_ +[1.45,2.014272114,sinh(1.45),sinh(1.45)-2.014272114],_ +[1.46,2.036861627,sinh(1.46),sinh(1.46)-2.036861627],_ +[1.47,2.059654828,sinh(1.47),sinh(1.47)-2.059654828],_ +[1.48,2.082653996,sinh(1.48),sinh(1.48)-2.082653996],_ +[1.49,2.105861432,sinh(1.49),sinh(1.49)-2.105861432],_ +[1.50,2.129279455,sinh(1.50),sinh(1.50)-2.129279455],_ 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[1.18,1.473547732,1.4735477321 442698057,0.1442698057 E -9], +--R [1.19,1.491429972,1.4914299716 582071144,- 0.3417928856 E -9], +--R [1.2,1.509461355,1.5094613554 121726964,0.4121726964 E -9], +--R [1.21,1.527643687,1.5276436865 595681515,- 0.4404318485 E -9], +--R [1.22,1.545978783,1.5459787833 486602124,0.3486602124 E -9], +--R [1.23,1.564468479,1.5644684793 044070864,0.3044070864 E -9], +--R [1.24,1.583114623,1.5831146234 118124797,0.4118124797 E -9], +--R [1.25,1.60191908,1.6019190803 008256379,0.3008256379 E -9], +--R [1.26,1.62088373,1.6208837304 328058954,0.4328058954 E -9], +--R [1.27,1.64001047,1.6400104702 88570378,0.288570378 E -9], +--R [1.28,1.659301213,1.6593012125 580436651,- 0.4419563349 E -9], +--R [1.29,1.678757886,1.6787578863 315283762,0.3315283762 E -9], +--R [1.3,1.698382437,1.6983824372 926158087,0.2926158087 E -9], +--R [1.31,1.718176828,1.7181768279 127559182,- 0.872440818 E -10], +--R [1.32,1.738143038,1.7381430376 475060993,- 0.3524939007 E -9], +--R [1.33,1.758283063,1.7582830631 344783905,0.1344783905 E -9], +--R [1.34,1.778598918,1.7785989183 930048997,0.3930048997 E -9], +--R [1.35,1.799092635,1.7990926350 255414153,0.255414153 E -10], +--R [1.36,1.819766262,1.8197662624 20829345,0.420829345 E -9], +--R [1.37,1.840621868,1.8406218679 588362979,- 0.411637021 E -10], +--R [1.38,1.861661537,1.8616615372 174958039,0.2174958039 E -9], +--R [1.39,1.882887374,1.8828873741 812668452,0.1812668451 E -9], +--R [1.4,1.904301501,1.9043015014 515340551,0.4515340551 E -9], +--R [1.41,1.92590606,1.9259060604 588696261,0.4588696261 E -9], +--R [1.42,1.947703212,1.9477032116 771781509,- 0.3228218491 E -9], +--R [1.43,1.969695135,1.9696951348 397458135,- 0.1602541865 E -9], +--R [1.44,1.991884029,1.9918840291 572155345,0.1572155345 E -9], +--R [1.45,2.014272114,2.0142721135 375098676,- 0.4624901324 E -9], +--R [1.46,2.036861627,2.0368616268 077236416,- 0.192276358 E -9], +--R [1.47,2.059654828,2.0596548279 380085349,- 0.619914651 E -10], +--R [1.48,2.082653996,2.0826539962 674719736,0.2674719736 E -9], +--R [1.49,2.105861432,2.1058614317 321129415,- 0.2678870585 E -9], +--R [1.5,2.129279455,2.1292794550 948174968,0.948174968 E -10], +--R [1.51,2.152910408,2.1529104081 774369945,0.177436994 E -9], +--R [1.52,2.176756654,2.1767566540 94972223,0.94972223 E -10], +--R [1.53,2.200820577,2.2008205774 918868736,0.4918868736 E -9], +--R [1.54,2.225104585,2.2251045847 805739743,- 0.219426026 E -9], +--R [1.55,2.249611104,2.2496111043 819991339,0.3819991339 E -9], +--R [1.56,2.274342587,2.2743425869 685446626,- 0.314553374 E -10], +--R [1.57,2.299301506,2.2993015057 090788526,- 0.2909211474 E -9], +--R [1.58,2.324490357,2.3244903565 162749255,- 0.4837250745 E -9], +--R [1.59,2.349911658,2.3499116582 962043799,0.2962043799 E -9], +--R [1.6,2.375567953,2.3755679532 002296976,0.200229698 E -9], +--R [1.61,2.401461807,2.4014618068 79221598,- 0.120778402 E -9], +--R [1.62,2.427595809,2.4275958087 401262638,- 0.2598737362 E -9], +--R [1.63,2.453972572,2.4539725722 049081927,0.204908193 E -9], +--R [1.64,2.480594735,2.4805947349 718945727,- 0.281054273 E -10], +--R [1.65,2.507464959,2.5074649592 795473117,0.2795473117 E -9], +--R [1.66,2.534585932,2.5345859321 726891034,0.172689103 E -9], +--R [1.67,2.561960366,2.5619603657 712101481,- 0.228789852 E -9], +--R [1.68,2.589590998,2.5895909975 412824018,- 0.4587175982 E -9], +--R [1.69,2.617480591,2.6174805905 69108475,- 0.430891525 E -9], +--R [1.7,2.645631934,2.6456319338 372325553,- 0.162767445 E -9], +--R [1.71,2.674047843,2.6740478425 034409861,- 0.4965590139 E -9], +--R [1.72,2.702731158,2.7027311581 822803909,0.182280391 E -9], +--R [1.73,2.731684749,2.7316847492 292214966,0.229221497 E -9], +--R [1.74,2.760911511,2.7609115110 274970701,0.274970701 E -10], +--R [1.75,2.790414366,2.7904143662 776426551,0.2776426551 E -9], +--R [1.76,2.820196265,2.8201962652 897690607,0.2897690607 E -9], +--R [1.77,2.850260186,2.8502601862 785958316,0.2785958316 E -9], +--R [1.78,2.880609136,2.8806091356 612752013,- 0.3387247987 E -9], +--R [1.79,2.911246148,2.9112461483 580363133,0.3580363133 E -9], +--R [1.8,2.942174288,2.9421742880 956797727,0.956797727 E -10], +--R [1.81,2.973396648,2.9733966477 139528796,- 0.2860471204 E -9], +--R [1.82,3.004916349,3.0049163494 748361809,0.4748361809 E -9], +--R [1.83,3.036736545,3.0367365453 747722708,0.3747722708 E -9], +--R [1.84,3.068860417,3.0688604174 598680611,0.4598680611 E -9], +--R [1.85,3.101291178,3.1012911781 441020441,0.144102044 E -9], +--R [1.86,3.134032071,3.1340320705 305683671,- 0.4694316329 E -9], +--R [1.87,3.167086369,3.1670863687 357898447,- 0.2642101554 E -9], +--R [1.88,3.200457378,3.2004573782 171323393,0.217132339 E -9], +--R [1.89,3.234148436,3.2341484361 033532526,0.103353253 E -9], +--R [1.9,3.268162912,3.2681629115 283171817,- 0.4716828183 E -9], +--R [1.91,3.302504206,3.3025042059 679121137,- 0.320878863 E -10], +--R [1.92,3.337175754,3.3371757535 801998489,- 0.4198001511 E -9], +--R [1.93,3.372181022,3.3721810215 488346686,- 0.4511653313 E -9], +--R [1.94,3.40752351,3.4075235104 297845903,0.4297845903 E -9], +--R [1.95,3.443206754,3.4432067545 013898812,0.5013898812 E -9], +--R [1.96,3.479234322,3.4792343221 177938377,0.117793838 E -9], +--R [1.97,3.515609816,3.5156098160 657811731,0.657811731 E -10], +--R [1.98,3.552336874,3.5523368739 25059699,- 0.74940301 E -10], +--R [1.99,3.589419168,3.5894191684 320213268,0.4320213268 E -9], +--R [2.0,3.626860408,3.6268604078 470187677,- 0.152981232 E -9]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of cosh, ranging from 0.00 to 2.00. The +second column is the reference value of sinh from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp213-216 + +<<*>>= +--S 2 of 2 +[[0.00,1.000000000,cosh(0.00),cosh(0.00)-1.000000000],_ +[0.01,1.000050000,cosh(0.01),cosh(0.01)-1.000050000],_ +[0.02,1.000200007,cosh(0.02),cosh(0.02)-1.000200007],_ +[0.03,1.000450034,cosh(0.03),cosh(0.03)-1.000450034],_ +[0.04,1.000800107,cosh(0.04),cosh(0.04)-1.000800107],_ +[0.05,1.001250260,cosh(0.05),cosh(0.05)-1.001250260],_ +[0.06,1.001800540,cosh(0.06),cosh(0.06)-1.001800540],_ +[0.07,1.002451001,cosh(0.07),cosh(0.07)-1.002451001],_ +[0.08,1.003201707,cosh(0.08),cosh(0.08)-1.003201707],_ +[0.09,1.004052734,cosh(0.09),cosh(0.09)-1.004052734],_ +[0.10,1.005004168,cosh(0.10),cosh(0.10)-1.005004168],_ +[0.11,1.006056103,cosh(0.11),cosh(0.11)-1.006056103],_ +[0.12,1.007208644,cosh(0.12),cosh(0.12)-1.007208644],_ +[0.13,1.008461907,cosh(0.13),cosh(0.13)-1.008461907],_ +[0.14,1.009816017,cosh(0.14),cosh(0.14)-1.009816017],_ +[0.15,1.011271110,cosh(0.15),cosh(0.15)-1.011271110],_ +[0.16,1.012827330,cosh(0.16),cosh(0.16)-1.012827330],_ +[0.17,1.014484834,cosh(0.17),cosh(0.17)-1.014484834],_ +[0.18,1.016243787,cosh(0.18),cosh(0.18)-1.016243787],_ +[0.19,1.018104366,cosh(0.19),cosh(0.19)-1.018104366],_ +[0.20,1.020066756,cosh(0.20),cosh(0.20)-1.020066756],_ +[0.21,1.022131153,cosh(0.21),cosh(0.21)-1.022131153],_ +[0.22,1.024297764,cosh(0.22),cosh(0.22)-1.024297764],_ +[0.23,1.026566806,cosh(0.23),cosh(0.23)-1.026566806],_ +[0.24,1.028938506,cosh(0.24),cosh(0.24)-1.028938506],_ +[0.25,1.031413100,cosh(0.25),cosh(0.25)-1.031413100],_ +[0.26,1.033990836,cosh(0.26),cosh(0.26)-1.033990836],_ +[0.27,1.036671973,cosh(0.27),cosh(0.27)-1.036671973],_ +[0.28,1.039456777,cosh(0.28),cosh(0.28)-1.039456777],_ +[0.29,1.042345528,cosh(0.29),cosh(0.29)-1.042345528],_ +[0.30,1.045338514,cosh(0.30),cosh(0.30)-1.045338514],_ +[0.31,1.048436035,cosh(0.31),cosh(0.31)-1.048436035],_ +[0.32,1.051638401,cosh(0.32),cosh(0.32)-1.051638401],_ +[0.33,1.054945931,cosh(0.33),cosh(0.33)-1.054945931],_ +[0.34,1.058358957,cosh(0.34),cosh(0.34)-1.058358957],_ +[0.35,1.061877819,cosh(0.35),cosh(0.35)-1.061877819],_ +[0.36,1.065502870,cosh(0.36),cosh(0.36)-1.065502870],_ +[0.37,1.069234473,cosh(0.37),cosh(0.37)-1.069234473],_ +[0.38,1.073072999,cosh(0.38),cosh(0.38)-1.073072999],_ +[0.39,1.077018834,cosh(0.39),cosh(0.39)-1.077018834],_ +[0.40,1.081072372,cosh(0.40),cosh(0.40)-1.081072372],_ +[0.41,1.085234018,cosh(0.41),cosh(0.41)-1.085234018],_ +[0.42,1.089504188,cosh(0.42),cosh(0.42)-1.089504188],_ +[0.43,1.093883309,cosh(0.43),cosh(0.43)-1.093883309],_ +[0.44,1.098371820,cosh(0.44),cosh(0.44)-1.098371820],_ +[0.45,1.102970169,cosh(0.45),cosh(0.45)-1.102970169],_ +[0.46,1.107678815,cosh(0.46),cosh(0.46)-1.107678815],_ +[0.47,1.112498231,cosh(0.47),cosh(0.47)-1.112498231],_ +[0.48,1.117428897,cosh(0.48),cosh(0.48)-1.117428897],_ +[0.49,1.122471307,cosh(0.49),cosh(0.49)-1.122471307],_ +[0.50,1.127625965,cosh(0.50),cosh(0.50)-1.127625965],_ +[0.51,1.132893387,cosh(0.51),cosh(0.51)-1.132893387],_ +[0.52,1.138274099,cosh(0.52),cosh(0.52)-1.138274099],_ +[0.53,1.143768639,cosh(0.53),cosh(0.53)-1.143768639],_ +[0.54,1.149377557,cosh(0.54),cosh(0.54)-1.149377557],_ +[0.55,1.155101414,cosh(0.55),cosh(0.55)-1.155101414],_ +[0.56,1.160940782,cosh(0.56),cosh(0.56)-1.160940782],_ +[0.57,1.166896245,cosh(0.57),cosh(0.57)-1.166896245],_ +[0.58,1.172968399,cosh(0.58),cosh(0.58)-1.172968399],_ +[0.59,1.179157850,cosh(0.59),cosh(0.59)-1.179157850],_ +[0.60,1.185465218,cosh(0.60),cosh(0.60)-1.185465218],_ +[0.61,1.191891134,cosh(0.61),cosh(0.61)-1.191891134],_ +[0.62,1.198436240,cosh(0.62),cosh(0.62)-1.198436240],_ +[0.63,1.205101190,cosh(0.63),cosh(0.63)-1.205101190],_ +[0.64,1.211886652,cosh(0.64),cosh(0.64)-1.211886652],_ +[0.65,1.218793303,cosh(0.65),cosh(0.65)-1.218793303],_ +[0.66,1.225821834,cosh(0.66),cosh(0.66)-1.225821834],_ +[0.67,1.232972949,cosh(0.67),cosh(0.67)-1.232972949],_ +[0.68,1.240247362,cosh(0.68),cosh(0.68)-1.240247362],_ +[0.69,1.247645801,cosh(0.69),cosh(0.69)-1.247645801],_ +[0.70,1.255169006,cosh(0.70),cosh(0.70)-1.255169006],_ +[0.71,1.262817728,cosh(0.71),cosh(0.71)-1.262817728],_ +[0.72,1.270592733,cosh(0.72),cosh(0.72)-1.270592733],_ +[0.73,1.278494799,cosh(0.73),cosh(0.73)-1.278494799],_ +[0.74,1.286524715,cosh(0.74),cosh(0.74)-1.286524715],_ +[0.75,1.294683285,cosh(0.75),cosh(0.75)-1.294683285],_ +[0.76,1.302971324,cosh(0.76),cosh(0.76)-1.302971324],_ +[0.77,1.311389661,cosh(0.77),cosh(0.77)-1.311389661],_ +[0.78,1.319939138,cosh(0.78),cosh(0.78)-1.319939138],_ +[0.79,1.328620611,cosh(0.79),cosh(0.79)-1.328620611],_ +[0.80,1.337434946,cosh(0.80),cosh(0.80)-1.337434946],_ +[0.81,1.346383026,cosh(0.81),cosh(0.81)-1.346383026],_ +[0.82,1.355465746,cosh(0.82),cosh(0.82)-1.355465746],_ +[0.83,1.364684013,cosh(0.83),cosh(0.83)-1.364684013],_ +[0.84,1.374038750,cosh(0.84),cosh(0.84)-1.374038750],_ +[0.85,1.383530892,cosh(0.85),cosh(0.85)-1.383530892],_ +[0.86,1.393161388,cosh(0.86),cosh(0.86)-1.393161388],_ +[0.87,1.402931201,cosh(0.87),cosh(0.87)-1.402931201],_ +[0.88,1.412841309,cosh(0.88),cosh(0.88)-1.412841309],_ +[0.89,1.422892702,cosh(0.89),cosh(0.89)-1.422892702],_ +[0.90,1.433086385,cosh(0.90),cosh(0.90)-1.433086385],_ +[0.91,1.443423379,cosh(0.91),cosh(0.91)-1.443423379],_ +[0.92,1.453904716,cosh(0.92),cosh(0.92)-1.453904716],_ +[0.93,1.464531444,cosh(0.93),cosh(0.93)-1.464531444],_ +[0.94,1.475304627,cosh(0.94),cosh(0.94)-1.475304627],_ +[0.95,1.486225341,cosh(0.95),cosh(0.95)-1.486225341],_ +[0.96,1.497294680,cosh(0.96),cosh(0.96)-1.497294680],_ +[0.97,1.508513749,cosh(0.97),cosh(0.97)-1.508513749],_ +[0.98,1.519883670,cosh(0.98),cosh(0.98)-1.519883670],_ +[0.99,1.531405582,cosh(0.99),cosh(0.99)-1.531405582],_ +[1.00,1.543080635,cosh(1.00),cosh(1.00)-1.543080635],_ +[1.01,1.554909997,cosh(1.01),cosh(1.01)-1.554909997],_ +[1.02,1.566894852,cosh(1.02),cosh(1.02)-1.566894852],_ +[1.03,1.579036398,cosh(1.03),cosh(1.03)-1.579036398],_ +[1.04,1.591335848,cosh(1.04),cosh(1.04)-1.591335848],_ +[1.05,1.603794434,cosh(1.05),cosh(1.05)-1.603794434],_ +[1.06,1.616413400,cosh(1.06),cosh(1.06)-1.616413400],_ +[1.07,1.629194009,cosh(1.07),cosh(1.07)-1.629194009],_ +[1.08,1.642137538,cosh(1.08),cosh(1.08)-1.642137538],_ +[1.09,1.655245283,cosh(1.09),cosh(1.09)-1.655245283],_ +[1.10,1.668518554,cosh(1.10),cosh(1.10)-1.668518554],_ +[1.11,1.681958678,cosh(1.11),cosh(1.11)-1.681958678],_ +[1.12,1.695566999,cosh(1.12),cosh(1.12)-1.695566999],_ +[1.13,1.709344878,cosh(1.13),cosh(1.13)-1.709344878],_ +[1.14,1.723293694,cosh(1.14),cosh(1.14)-1.723293694],_ +[1.15,1.737414840,cosh(1.15),cosh(1.15)-1.737414840],_ +[1.16,1.751709728,cosh(1.16),cosh(1.16)-1.751709728],_ +[1.17,1.766179790,cosh(1.17),cosh(1.17)-1.766179790],_ +[1.18,1.780826471,cosh(1.18),cosh(1.18)-1.780826471],_ +[1.19,1.795651236,cosh(1.19),cosh(1.19)-1.795651236],_ +[1.20,1.810655567,cosh(1.20),cosh(1.20)-1.810655567],_ +[1.21,1.825840966,cosh(1.21),cosh(1.21)-1.825840966],_ +[1.22,1.841208950,cosh(1.22),cosh(1.22)-1.841208950],_ +[1.23,1.856761057,cosh(1.23),cosh(1.23)-1.856761057],_ +[1.24,1.872498841,cosh(1.24),cosh(1.24)-1.872498841],_ +[1.25,1.888423877,cosh(1.25),cosh(1.25)-1.888423877],_ +[1.26,1.904537757,cosh(1.26),cosh(1.26)-1.904537757],_ +[1.27,1.920842092,cosh(1.27),cosh(1.27)-1.920842092],_ +[1.28,1.937338513,cosh(1.28),cosh(1.28)-1.937338513],_ +[1.29,1.954028669,cosh(1.29),cosh(1.29)-1.954028669],_ +[1.30,1.970914230,cosh(1.30),cosh(1.30)-1.970914230],_ +[1.31,1.987996884,cosh(1.31),cosh(1.31)-1.987996884],_ +[1.32,2.005278340,cosh(1.32),cosh(1.32)-2.005278340],_ +[1.33,2.022760324,cosh(1.33),cosh(1.33)-2.022760324],_ +[1.34,2.040444587,cosh(1.34),cosh(1.34)-2.040444587],_ +[1.35,2.058332896,cosh(1.35),cosh(1.35)-2.058332896],_ +[1.36,2.076427039,cosh(1.36),cosh(1.36)-2.076427039],_ +[1.37,2.094728828,cosh(1.37),cosh(1.37)-2.094728828],_ +[1.38,2.113240090,cosh(1.38),cosh(1.38)-2.113240090],_ +[1.39,2.131962679,cosh(1.39),cosh(1.39)-2.131962679],_ +[1.40,2.150898465,cosh(1.40),cosh(1.40)-2.150898465],_ +[1.41,2.170049344,cosh(1.41),cosh(1.41)-2.170049344],_ +[1.42,2.189417229,cosh(1.42),cosh(1.42)-2.189417229],_ +[1.43,2.209004057,cosh(1.43),cosh(1.43)-2.209004057],_ +[1.44,2.228811788,cosh(1.44),cosh(1.44)-2.228811788],_ +[1.45,2.248842402,cosh(1.45),cosh(1.45)-2.248842402],_ +[1.46,2.269097902,cosh(1.46),cosh(1.46)-2.269097902],_ +[1.47,2.289580313,cosh(1.47),cosh(1.47)-2.289580313],_ +[1.48,2.310291685,cosh(1.48),cosh(1.48)-2.310291685],_ +[1.49,2.331234087,cosh(1.49),cosh(1.49)-2.331234087],_ +[1.50,2.352409615,cosh(1.50),cosh(1.50)-2.352409615],_ +[1.51,2.373820386,cosh(1.51),cosh(1.51)-2.373820386],_ +[1.52,2.395468541,cosh(1.52),cosh(1.52)-2.395468541],_ +[1.53,2.417356245,cosh(1.53),cosh(1.53)-2.417356245],_ +[1.54,2.439485686,cosh(1.54),cosh(1.54)-2.439485686],_ +[1.55,2.461859078,cosh(1.55),cosh(1.55)-2.461859078],_ +[1.56,2.484478658,cosh(1.56),cosh(1.56)-2.484478658],_ +[1.57,2.507346688,cosh(1.57),cosh(1.57)-2.507346688],_ +[1.58,2.530465455,cosh(1.58),cosh(1.58)-2.530465455],_ +[1.59,2.553837270,cosh(1.59),cosh(1.59)-2.553837270],_ +[1.60,2.577464471,cosh(1.60),cosh(1.60)-2.577464471],_ +[1.61,2.601349421,cosh(1.61),cosh(1.61)-2.601349421],_ +[1.62,2.625494508,cosh(1.62),cosh(1.62)-2.625494508],_ +[1.63,2.649902146,cosh(1.63),cosh(1.63)-2.649902146],_ +[1.64,2.674574777,cosh(1.64),cosh(1.64)-2.674574777],_ +[1.65,2.699514868,cosh(1.65),cosh(1.65)-2.699514868],_ +[1.66,2.724724912,cosh(1.66),cosh(1.66)-2.724724912],_ +[1.67,2.750207431,cosh(1.67),cosh(1.67)-2.750207431],_ +[1.68,2.775964974,cosh(1.68),cosh(1.68)-2.775964974],_ +[1.69,2.802000115,cosh(1.69),cosh(1.69)-2.802000115],_ +[1.70,2.828315458,cosh(1.70),cosh(1.70)-2.828315458],_ +[1.71,2.854913635,cosh(1.71),cosh(1.71)-2.854913635],_ +[1.72,2.881797306,cosh(1.72),cosh(1.72)-2.881797306],_ +[1.73,2.908969159,cosh(1.73),cosh(1.73)-2.908969159],_ +[1.74,2.936431912,cosh(1.74),cosh(1.74)-2.936431912],_ +[1.75,2.964188310,cosh(1.75),cosh(1.75)-2.964188310],_ +[1.76,2.992241129,cosh(1.76),cosh(1.76)-2.992241129],_ +[1.77,3.020593175,cosh(1.77),cosh(1.77)-3.020593175],_ +[1.78,3.049247283,cosh(1.78),cosh(1.78)-3.049247283],_ +[1.79,3.078206318,cosh(1.79),cosh(1.79)-3.078206318],_ +[1.80,3.107473176,cosh(1.80),cosh(1.80)-3.107473176],_ +[1.81,3.137050785,cosh(1.81),cosh(1.81)-3.137050785],_ +[1.82,3.166942100,cosh(1.82),cosh(1.82)-3.166942100],_ +[1.83,3.197150113,cosh(1.83),cosh(1.83)-3.197150113],_ +[1.84,3.227677844,cosh(1.84),cosh(1.84)-3.227677844],_ +[1.85,3.258528344,cosh(1.85),cosh(1.85)-3.258528344],_ +[1.86,3.289704701,cosh(1.86),cosh(1.86)-3.289704701],_ +[1.87,3.321210031,cosh(1.87),cosh(1.87)-3.321210031],_ +[1.88,3.353047484,cosh(1.88),cosh(1.88)-3.353047484],_ +[1.89,3.385220245,cosh(1.89),cosh(1.89)-3.385220245],_ +[1.90,3.417731531,cosh(1.90),cosh(1.90)-3.417731531],_ +[1.91,3.450584593,cosh(1.91),cosh(1.91)-3.450584593],_ +[1.92,3.483782716,cosh(1.92),cosh(1.92)-3.483782716],_ +[1.93,3.517329220,cosh(1.93),cosh(1.93)-3.517329220],_ +[1.94,3.551227460,cosh(1.94),cosh(1.94)-3.551227460],_ +[1.95,3.585480826,cosh(1.95),cosh(1.95)-3.585480826],_ +[1.96,3.620092743,cosh(1.96),cosh(1.96)-3.620092743],_ +[1.97,3.655066672,cosh(1.97),cosh(1.97)-3.655066672],_ +[1.98,3.690406111,cosh(1.98),cosh(1.98)-3.690406111],_ +[1.99,3.726114594,cosh(1.99),cosh(1.99)-3.726114594],_ +[2.00,3.762195691,cosh(2.00),cosh(2.00)-3.762195691]] +--R +--R +--R (2) +--R [[0.0,1.0,1.0,0.0], [0.01,1.00005,1.0000500004 166680556,0.4166680556 E -9], +--R [0.02,1.000200007,1.0002000066 667555562,- 0.3332444438 E -9], +--R [0.03,1.000450034,1.0004500337 510125163,- 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665410931,0.2665410931 E -9], +--R [0.19,1.018104366,1.0181043658 003068879,- 0.1996931121 E -9], +--R [0.2,1.020066756,1.0200667556 190758463,- 0.3809241537 E -9], +--R [0.21,1.022131153,1.0221311529 634651755,- 0.365348245 E -10], +--R [0.22,1.024297764,1.0242977642 749296513,0.2749296512 E -9], +--R [0.23,1.026566806,1.0265668062 164059355,0.2164059355 E -9], +--R [0.24,1.028938506,1.0289385056 939790504,- 0.3060209496 E -9], +--R [0.25,1.0314131,1.0314130998 795731762,- 0.1204268238 E -9], +--R [0.26,1.033990836,1.0339908362 346690408,0.2346690408 E -9], +--R [0.27,1.036671973,1.0366719725 350502748,- 0.4649497252 E -9], +--R [0.28,1.039456777,1.0394567768 965812039,- 0.103418796 E -9], +--R [0.29,1.042345528,1.0423455278 020186592,- 0.1979813408 E -9], +--R [0.3,1.045338514,1.0453385141 28860485,0.128860485 E -9], +--R [0.31,1.048436035,1.0484360351 78233529,0.178233529 E -9], +--R [0.32,1.051638401,1.0516384007 048240047,- 0.2951759953 E -9], +--R [0.33,1.054945931,1.0549459309 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[0.48,1.117428897,1.1174288969 995171175,- 0.4828825 E -12], +--R [0.49,1.122471307,1.1224713070 698975196,0.698975196 E -10], +--R [0.5,1.127625965,1.1276259652 063807852,0.2063807852 E -9], +--R [0.51,1.132893387,1.1328933868 790761256,- 0.1209238744 E -9], +--R [0.52,1.138274099,1.1382740988 345403429,- 0.1654596571 E -9], +--R [0.53,1.143768639,1.1437686391 484529252,0.1484529252 E -9], +--R [0.54,1.149377557,1.1493775572 794240625,0.2794240625 E -9], +--R [0.55,1.155101414,1.1551014141 239409661,0.1239409661 E -9], +--R [0.56,1.160940782,1.1609407820 724579841,0.724579841 E -10], +--R [0.57,1.166896245,1.1668962450 666361245,0.666361245 E -10], +--R [0.58,1.172968399,1.1729683986 577377074,- 0.3422622926 E -9], +--R [0.59,1.17915785,1.1791578500 661819879,0.661819879 E -10], +--R [0.6,1.185465218,1.1854652182 422677038,0.2422677038 E -9], +--R [0.61,1.191891134,1.1918911339 280686212,- 0.719313788 E -10], +--R [0.62,1.19843624,1.1984362397 20508268,- 0.279491732 E -9], +--R [0.63,1.20510119,1.2051011901 35620161,0.135620161 E -9], +--R [0.64,1.211886652,1.2118866516 739999553,- 0.3260000447 E -9], +--R [0.65,1.218793303,1.2187933028 87456059,- 0.112543941 E -9], +--R [0.66,1.225821834,1.2258218344 468653796,0.4468653796 E -9], +--R [0.67,1.232972949,1.2329729492 112409872,0.2112409872 E -9], +--R [0.68,1.240247362,1.2402473622 980186015,0.2980186015 E -9], +--R [0.69,1.247645801,1.2476458011 545689314,0.1545689314 E -9], +--R [0.7,1.255169006,1.2551690056 309430182,- 0.3690569818 E -9], +--R [0.71,1.262817728,1.2628177280 538578572,0.538578572 E -10], +--R [0.72,1.270592733,1.2705927333 019296965,0.3019296965 E -9], +--R [0.73,1.278494799,1.2784947988 82162536,- 0.117837464 E -9], +--R [0.74,1.286524715,1.2865247150 076994755,0.769947551 E -11], +--R [0.75,1.294683285,1.2946832846 768446878,- 0.3231553122 E -9], +--R [0.76,1.302971324,1.3029713237 533639182,- 0.2466360818 E -9], +--R [0.77,1.311389661,1.3113896610 480715408,0.480715408 E -10], +--R [0.78,1.319939138,1.3199391384 017123309,0.4017123309 E -9], +--R [0.79,1.328620611,1.3286206107 691462407,- 0.2308537593 E -9], +--R [0.8,1.337434946,1.3374349463 04844598,0.304844598 E -9], +--R [0.81,1.346383026,1.3463830264 497062768,0.4497062768 E -9], +--R [0.82,1.355465746,1.3554657460 192025216,0.192025216 E -10], +--R [0.83,1.364684013,1.3646840132 928592402,0.2928592402 E -9], +--R [0.84,1.37403875,1.3740387501 050857132,0.105085713 E -9], +--R [0.85,1.383530892,1.3835308919 373588034,- 0.626411966 E -10], +--R [0.86,1.393161388,1.3931613880 117718825,0.117718825 E -10], +--R [0.87,1.402931201,1.4029312013 859578321,0.3859578321 E -9], +--R [0.88,1.412841309,1.4128413090 493956089,0.493956089 E -10], +--R [0.89,1.422892702,1.4228927020 211100075,0.211100075 E -10], +--R [0.9,1.433086385,1.4330863854 487743878,0.4487743878 E -9], +--R [0.91,1.443423379,1.4434233787 09226281,- 0.290773719 E -9], +--R [0.92,1.453904716,1.4539047155 104059219,- 0.4895940781 E -9], +--R [0.93,1.464531444,1.4645314439 947279049,- 0.52720951 E -11], +--R [0.94,1.475304627,1.4753046268 438962989,- 0.1561037011 E -9], +--R [0.95,1.486225341,1.4862253413 85173703,0.385173703 E -9], +--R [0.96,1.49729468,1.4972946796 991148706,- 0.3008851294 E -9], +--R [0.97,1.508513749,1.5085137487 287756753,- 0.2712243247 E -9], +--R [0.98,1.51988367,1.5198836703 904083385,0.3904083385 E -9], +--R [0.99,1.531405582,1.5314055816 856539898,- 0.3143460102 E -9], +--R [1.0,1.543080635,1.5430806348 152437785,- 0.1847562215 E -9], +--R [1.01,1.554909997,1.5549099972 942199069,0.2942199069 E -9], +--R [1.02,1.566894852,1.5668948520 686881075,0.686881075 E -10], +--R [1.03,1.579036398,1.5790363976 341132396,- 0.3658867604 E -9], +--R [1.04,1.591335848,1.5913358481 551698338,0.1551698338 E -9], +--R [1.05,1.603794434,1.6037944335 871595723,- 0.4128404277 E -9], +--R [1.06,1.6164134,1.6164133997 99007843,- 0.200992157 E -9], +--R [1.07,1.629194009,1.6291940086 97851671,- 0.302148329 E -9], +--R [1.08,1.642137538,1.6421375383 552314837,0.3552314837 E -9], +--R [1.09,1.655245283,1.6552452831 348993296,0.1348993296 E -9], +--R [1.1,1.668518554,1.6685185538 222563327,- 0.1777436673 E -9], +--R [1.11,1.681958678,1.6819586777 554323243,- 0.2445676757 E -9], +--R [1.12,1.695566999,1.6955669989 580207628,- 0.419792372 E -10], +--R [1.13,1.709344878,1.7093448782 734822124,0.2734822124 E -9], +--R [1.14,1.723293694,1.7232936935 012298237,- 0.4987701763 E -9], +--R [1.15,1.73741484,1.7374148395 344104227,- 0.4655895773 E -9], +--R [1.16,1.751709728,1.7517097284 993949886,0.4993949886 E -9], +--R [1.17,1.76617979,1.7661797898 96992467,- 0.103007533 E -9], +--R [1.18,1.780826471,1.7808264707 454010422,- 0.2545989578 E -9], +--R [1.19,1.795651236,1.7956512357 249111632,- 0.2750888368 E -9], +--R [1.2,1.810655567,1.8106555673 243747931,0.3243747931 E -9], +--R [1.21,1.825840966,1.8258409659 894555295,- 0.105444705 E -10], +--R [1.22,1.84120895,1.8412089502 726744215,0.2726744215 E -9], +--R [1.23,1.856761057,1.8567610569 852664874,- 0.147335126 E -10], +--R [1.24,1.872498841,1.8724988413 508631184,0.3508631184 E -9], +--R [1.25,1.888423877,1.8884238771 610157382,0.1610157382 E -9], +--R [1.26,1.904537757,1.9045377569 325762696,- 0.674237304 E -10], +--R [1.27,1.920842092,1.9208420920 669501464,0.669501464 E -10], +--R [1.28,1.937338513,1.9373385130 112377973,0.112377973 E -10], +--R [1.29,1.954028669,1.9540286694 212807143,0.4212807143 E -9], +--R [1.3,1.97091423,1.9709142303 266284118,0.3266284118 E -9], +--R [1.31,1.987996884,1.9879968842 974427722,0.2974427722 E -9], +--R [1.32,2.00527834,2.0052783396 133564693,- 0.3866435307 E -9], +--R [1.33,2.022760324,2.0227603244 343023553,0.4343023553 E -9], +--R [1.34,2.040444587,2.0404445869 73330894,- 0.26669106 E -10], +--R [1.35,2.058332896,2.0583328956 714329229,- 0.3285670771 E -9], +--R [1.36,2.076427039,2.0764270393 743852257,0.3743852257 E -9], +--R [1.37,2.094728828,2.0947288275 11636601,- 0.488363399 E -9], +--R [1.38,2.11324009,2.1132400902 77252315,0.277252315 E -9], +--R [1.39,2.131962679,2.1319626788 129350329,- 0.187064967 E -9], +--R [1.4,2.150898465,2.1508984653 931405321,0.3931405321 E -9], +--R [1.41,2.170049344,2.1700493436 123067079,- 0.3876932921 E -9], +--R [1.42,2.189417229,2.1894172285 742145953,- 0.4257854047 E -9], +--R [1.43,2.209004057,2.2090040570 835003431,0.83500343 E -10], +--R [1.44,2.228811788,2.2288117878 393372912,- 0.160662709 E -9], +--R [1.45,2.248842402,2.2488424016 313075208,- 0.3686924792 E -9], +--R [1.46,2.269097902,2.2690979015 374824626,- 0.4625175374 E -9], +--R [1.47,2.289580313,2.2895803131 247323736,0.124732374 E -9], +--R [1.48,2.310291685,2.3102916846 512847122,- 0.3487152878 E -9], +--R [1.49,2.331234087,2.3312340872 715516672,0.2715516672 E -9], +--R [1.5,2.352409615,2.3524096152 432473258,0.2432473258 E -9], +--R [1.51,2.373820386,2.3738203861 368151896,0.13681519 E -9], +--R [1.52,2.395468541,2.3954685410 47186984,0.47186984 E -10], +--R [1.53,2.417356245,2.4173562448 078939354,- 0.192106065 E -9], +--R [1.54,2.439485686,2.4394856862 075519285,0.207551928 E -9], +--R [1.55,2.461859078,2.4618590782 087421916,0.208742192 E -9], +--R [1.56,2.484478658,2.4844786581 693093993,0.169309399 E -9], +--R [1.57,2.507346688,2.5073466880 66099321,0.66099321 E -10], +--R [1.58,2.530465455,2.5304654547 21158391,- 0.278841609 E -9], +--R [1.59,2.55383727,2.5538372700 304178181,0.304178181 E -10], +--R [1.6,2.577464471,2.5774644711 948851061,0.194885106 E -9], +--R [1.61,2.601349421,2.6013494209 543661015,- 0.456338985 E -10], +--R [1.62,2.625494508,2.6254945078 237409436,- 0.176259056 E -9], +--R [1.63,2.649902146,2.6499021463 318175428,0.3318175428 E -9], +--R [1.64,2.674574777,2.6745747772 627864732,0.2627864732 E -9], +--R [1.65,2.699514868,2.6995148679 00301426,- 0.99698574 E -10], +--R [1.66,2.724724912,2.7247249122 742096308,0.2742096308 E -9], +--R [1.67,2.750207431,2.7502074314 099569189,0.4099569189 E -9], +--R [1.68,2.775964974,2.7759649735 806923683,- 0.4193076317 E -9], +--R [1.69,2.802000115,2.8020001145 620977426,- 0.4379022574 E -9], +--R [1.7,2.828315458,2.8283154578 899672055,- 0.110032794 E -9], +--R [1.71,2.854913635,2.8549136351 205630698,0.12056307 E -9], +--R [1.72,2.881797306,2.8817973060 937736167,0.937736167 E -10], +--R [1.73,2.908969159,2.9089691591 990993011,0.199099301 E -9], +--R [1.74,2.936431912,2.9364319116 444939418,- 0.3555060582 E -9], +--R [1.75,2.96418831,2.9641883097 280877818,- 0.2719122182 E -9], +--R [1.76,2.992241129,2.9922411291 128195891,0.112819589 E -9], +--R [1.77,3.020593175,3.0205931751 040052646,0.104005265 E -9], +--R [1.78,3.049247283,3.0492472829 298707103,- 0.701292897 E -10], +--R [1.79,3.078206318,3.0782063180 250770157,0.250770157 E -10], +--R [1.8,3.107473176,3.1074731763 17266311,0.317266311 E -9], +--R [1.81,3.137050785,3.1370507845 166569452,- 0.4833430548 E -9], +--R [1.82,3.1669421,3.1669421004 087169461,0.4087169461 E -9], +--R [1.83,3.197150113,3.1971501131 499450329,0.149945033 E -9], +--R [1.84,3.227677844,3.2276778435 667887561,- 0.4332112439 E -9], +--R [1.85,3.258528344,3.2585283444 577296603,0.4577296603 E -9], +--R [1.86,3.289704701,3.2897047008 98565676,- 0.101434324 E -9], +--R [1.87,3.321210031,3.3212100305 509212704,- 0.4490787296 E -9], +--R [1.88,3.353047484,3.3530474839 74016208,- 0.25983792 E -10], +--R [1.89,3.385220245,3.3852202449 397240979,- 0.602759021 E -10], +--R [1.9,3.417731531,3.4177315307 509522343,- 0.2490477656 E -9], +--R [1.91,3.450584593,3.4505845925 633745687,- 0.4366254312 E -9], +--R [1.92,3.483782716,3.4837827157 105499861,- 0.289450014 E -9], +--R [1.93,3.51732922,3.5173292200 324583986,0.324583986 E -10], +--R [1.94,3.55122746,3.5512274602 074875108,0.207487511 E -9], +--R [1.95,3.585480826,3.5854808260 879034531,0.879034531 E -10], +--R [1.96,3.620092743,3.6200927430 388388338,0.388388338 E -10], +--R [1.97,3.655066672,3.6550666722 808321068,0.2808321068 E -9], +--R [1.98,3.690406111,3.6904061112 359525095,0.2359525095 E -9], +--R [1.99,3.726114594,3.7261145938 775451847,- 0.122454815 E -9], +--R [2.0,3.762195691,3.7621956910 836314596,0.836314596 E -10]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ + +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf Digital Library of Mathematical Functions}, +http://dlmf.nist.gov +\bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp213-216 +\end{thebibliography} +\end{document} diff --git a/src/input/tancot.input.pamphlet b/src/input/tancot.input.pamphlet new file mode 100644 index 0000000..8ef163c --- /dev/null +++ b/src/input/tancot.input.pamphlet @@ -0,0 +1,696 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input tancot.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This compares Axiom's tan and cot functions with the tables published in +Abramowitz and Stegun. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of tan(x), ranging from 0.01 to 1.60. The +second column is the reference value of tan from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp186-188 +<<*>>= +)spool tancot.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.01,0.010000333,tan(0.01),tan(0.01)-(0.010000333)],_ +[0.02,0.020002667,tan(0.02),tan(0.02)-(0.020002667)],_ +[0.03,0.030009003,tan(0.03),tan(0.03)-(0.030009003)],_ +[0.04,0.040021347,tan(0.04),tan(0.04)-(0.040021347)],_ +[0.05,0.050041708,tan(0.05),tan(0.05)-(0.050041708)],_ +[0.06,0.060072104,tan(0.06),tan(0.06)-(0.060072104)],_ +[0.07,0.070114558,tan(0.07),tan(0.07)-(0.070114558)],_ +[0.08,0.080171105,tan(0.08),tan(0.08)-(0.080171105)],_ +[0.09,0.090243790,tan(0.09),tan(0.09)-(0.090243790)],_ +[0.10,0.10033467,tan(0.10),tan(0.10)-(0.10033467)],_ +[0.11,0.11044582,tan(0.11),tan(0.11)-(0.11044582)],_ +[0.12,0.12057934,tan(0.12),tan(0.12)-(0.12057934)],_ +[0.13,0.13073732,tan(0.13),tan(0.13)-(0.13073732)],_ +[0.14,0.14092189,tan(0.14),tan(0.14)-(0.14092189)],_ +[0.15,0.15113522,tan(0.15),tan(0.15)-(0.15113522)],_ +[0.16,0.16137946,tan(0.16),tan(0.16)-(0.16137946)],_ +[0.17,0.17165682,tan(0.17),tan(0.17)-(0.17165682)],_ +[0.18,0.18196953,tan(0.18),tan(0.18)-(0.18196953)],_ +[0.19,0.19231984,tan(0.19),tan(0.19)-(0.19231984)],_ +[0.20,0.20271004,tan(0.20),tan(0.20)-(0.20271004)],_ +[0.21,0.21314244,tan(0.21),tan(0.21)-(0.21314244)],_ +[0.22,0.22361942,tan(0.22),tan(0.22)-(0.22361942)],_ +[0.23,0.23414336,tan(0.23),tan(0.23)-(0.23414336)],_ +[0.24,0.24471670,tan(0.24),tan(0.24)-(0.24471670)],_ +[0.25,0.25534192,tan(0.25),tan(0.25)-(0.25534192)],_ +[0.26,0.26602154,tan(0.26),tan(0.26)-(0.26602154)],_ +[0.27,0.27675814,tan(0.27),tan(0.27)-(0.27675814)],_ +[0.28,0.28755433,tan(0.28),tan(0.28)-(0.28755433)],_ +[0.29,0.29841279,tan(0.29),tan(0.29)-(0.29841279)],_ +[0.30,0.30933625,tan(0.30),tan(0.30)-(0.30933625)],_ +[0.31,0.32032751,tan(0.31),tan(0.31)-(0.32032751)],_ +[0.32,0.33138941,tan(0.32),tan(0.32)-(0.33138941)],_ +[0.33,0.34252487,tan(0.33),tan(0.33)-(0.34252487)],_ +[0.34,0.35373688,tan(0.34),tan(0.34)-(0.35373688)],_ +[0.35,0.36502849,tan(0.35),tan(0.35)-(0.36502849)],_ +[0.36,0.37640285,tan(0.36),tan(0.36)-(0.37640285)],_ +[0.37,0.38786316,tan(0.37),tan(0.37)-(0.38786316)],_ +[0.38,0.39941272,tan(0.38),tan(0.38)-(0.39941272)],_ +[0.39,0.41105492,tan(0.39),tan(0.39)-(0.41105492)],_ +[0.40,0.42279322,tan(0.40),tan(0.40)-(0.42279322)],_ +[0.41,0.43463120,tan(0.41),tan(0.41)-(0.43463120)],_ +[0.42,0.44657255,tan(0.42),tan(0.42)-(0.44657255)],_ +[0.43,0.45862102,tan(0.43),tan(0.43)-(0.45862102)],_ +[0.44,0.47078053,tan(0.44),tan(0.44)-(0.47078053)],_ +[0.45,0.48305507,tan(0.45),tan(0.45)-(0.48305507)],_ +[0.46,0.49544877,tan(0.46),tan(0.46)-(0.49544877)],_ +[0.47,0.50796590,tan(0.47),tan(0.47)-(0.50796590)],_ +[0.48,0.52061084,tan(0.48),tan(0.48)-(0.52061084)],_ +[0.49,0.53338815,tan(0.49),tan(0.49)-(0.53338815)],_ +[0.50,0.54630249,tan(0.50),tan(0.50)-(0.54630249)],_ +[0.51,0.55935872,tan(0.51),tan(0.51)-(0.55935872)],_ +[0.52,0.57256183,tan(0.52),tan(0.52)-(0.57256183)],_ +[0.53,0.58591701,tan(0.53),tan(0.53)-(0.58591701)],_ +[0.54,0.59942962,tan(0.54),tan(0.54)-(0.59942962)],_ +[0.55,0.61310521,tan(0.55),tan(0.55)-(0.61310521)],_ +[0.56,0.62694954,tan(0.56),tan(0.56)-(0.62694954)],_ +[0.57,0.64096855,tan(0.57),tan(0.57)-(0.64096855)],_ +[0.58,0.65516845,tan(0.58),tan(0.58)-(0.65516845)],_ +[0.59,0.66955565,tan(0.59),tan(0.59)-(0.66955565)],_ +[0.60,0.68413681,tan(0.60),tan(0.60)-(0.68413681)],_ +[0.61,0.69891886,tan(0.61),tan(0.61)-(0.69891886)],_ +[0.62,0.71390901,tan(0.62),tan(0.62)-(0.71390901)],_ +[0.63,0.72911473,tan(0.63),tan(0.63)-(0.72911473)],_ +[0.64,0.74454382,tan(0.64),tan(0.64)-(0.74454382)],_ +[0.65,0.76020440,tan(0.65),tan(0.65)-(0.76020440)],_ +[0.66,0.77610491,tan(0.66),tan(0.66)-(0.77610491)],_ +[0.67,0.79225417,tan(0.67),tan(0.67)-(0.79225417)],_ +[0.68,0.80866138,tan(0.68),tan(0.68)-(0.80866138)],_ +[0.69,0.82533611,tan(0.69),tan(0.69)-(0.82533611)],_ 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+[0.88,1.20966412,tan(0.88),tan(0.88)-(1.20966412)],_ +[0.89,1.23459946,tan(0.89),tan(0.89)-(1.23459946)],_ +[0.90,1.26015822,tan(0.90),tan(0.90)-(1.26015822)],_ +[0.91,1.28636938,tan(0.91),tan(0.91)-(1.28636938)],_ +[0.92,1.31326370,tan(0.92),tan(0.92)-(1.31326370)],_ +[0.93,1.34087383,tan(0.93),tan(0.93)-(1.34087383)],_ +[0.94,1.36923448,tan(0.94),tan(0.94)-(1.36923448)],_ +[0.95,1.39838259,tan(0.95),tan(0.95)-(1.39838259)],_ +[0.96,1.42835749,tan(0.96),tan(0.96)-(1.42835749)],_ +[0.97,1.45920113,tan(0.97),tan(0.97)-(1.45920113)],_ +[0.98,1.49095827,tan(0.98),tan(0.98)-(1.49095827)],_ +[0.99,1.52367674,tan(0.99),tan(0.99)-(1.52367674)],_ +[1.00,1.55740772,tan(1.00),tan(1.00)-(1.55740772)],_ +[1.01,1.5922060,tan(1.01),tan(1.01)-(1.5922060)],_ +[1.02,1.6281304,tan(1.02),tan(1.02)-(1.6281304)],_ +[1.03,1.6652440,tan(1.03),tan(1.03)-(1.6652440)],_ +[1.04,1.7036146,tan(1.04),tan(1.04)-(1.7036146)],_ +[1.05,1.7433153,tan(1.05),tan(1.05)-(1.7433153)],_ 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[1.02,1.6281304,1.6281304122 125526001,0.1221255260 01 E -7], +--R [1.03,1.665244,1.6652439932 315124346,- 0.6768487565 4 E -8], +--R [1.04,1.7036146,1.7036146122 591331094,0.1225913310 94 E -7], +--R [1.05,1.7433153,1.7433153099 831702625,0.9983170262 47 E -8], +--R [1.06,1.7844248,1.7844248315 940126524,0.3159401265 24 E -7], +--R [1.07,1.8270282,1.8270281965 348367381,- 0.3465163261 9 E -8], +--R [1.08,1.8712173,1.8712173378 97878195,0.3789787819 5 E -7], +--R [1.09,1.9170918,1.9170918216 068594024,0.2160685940 24 E -7], +--R [1.1,1.9647597,1.9647596572 486519509,- 0.4275134804 91 E -7], +--R [1.11,2.0143382,2.0143382144 768273135,0.1447682731 3 E -7], +--R [1.12,2.0659553,2.0659552613 80510241,- 0.3861948975 9 E -7], +--R [1.13,2.1197501,2.1197501441 871810139,0.4418718101 39 E -7], +--R [1.14,2.1758751,2.1758751312 648761686,0.3126487616 86 E -7], +--R [1.15,2.2344969,2.2344969487 553259802,0.4875532598 02 E -7], +--R [1.16,2.2957985,2.2957985404 922076011,0.4049220760 11 E -7], +--R [1.17,2.3599811,2.3599810913 765482032,- 0.8623451796 7 E -8], +--R [1.18,2.4272664,2.4272663614 002235775,- 0.3859977642 25 E -7], +--R [1.19,2.4978994,2.4978993874 226530062,- 0.1257734699 4 E -7], +--R [1.2,2.5721516,2.5721516221 263189354,0.2212631893 54 E -7], +--R [1.21,2.6503246,2.6503245949 706014665,- 0.5029398533 5 E -8], +--R [1.22,2.7327542,2.7327541993 067149987,- 0.6932850013 E -9], +--R [1.23,2.8198157,2.8198157342 681519748,0.3426815197 48 E -7], +--R [1.24,2.9119299,2.9119298611 552260267,- 0.3884477397 34 E -7], +--R [1.25,3.0095697,3.0095696738 628312882,- 0.2613716871 18 E -7], +--R [1.26,3.1132691,3.1132691342 651312093,0.3426513120 93 E -7], +--R [1.27,3.2236332,3.2236331902 040711359,- 0.9795928864 E -8], +--R [1.28,3.34135,3.3413499811 153736983,- 0.1888462630 17 E -7], +--R [1.29,3.4672057,3.4672056517 213857853,- 0.4827861421 47 E -7], +--R [1.3,3.6021024,3.6021024479 679781512,0.4796797815 12 E -7], +--R [1.31,3.747081,3.7470809761 884290733,- 0.2381157092 67 E -7], +--R [1.32,3.9033478,3.9033477874 966235656,- 0.1250337643 4 E -7], +--R [1.33,4.0723098,4.0723098354 650698554,0.3546506985 54 E -7], +--R [1.34,4.2556179,4.2556178917 394653427,- 0.8260534657 3 E -8], +--R [1.35,4.4552218,4.4552217595 627031753,- 0.4043729682 47 E -7], +--R [1.36,4.6734412,4.6734412029 885596449,0.2988559645 E -8], +--R [1.37,4.9130581,4.9130580704 624720101,- 0.2953752799 E -7], +--R [1.38,5.1774374,5.1774373886 304102949,- 0.1136958970 5 E -7], +--R [1.39,5.4706886,5.4706886429 532054937,0.4295320549 37 E -7], +--R [1.4,5.7978837,5.7978837154 828896437,0.1548288964 4 E -7], +--R [1.41,6.1653561,6.1653561445 520255476,0.4455202554 75 E -7], +--R [1.42,6.5811195,6.5811194561 942543239,- 0.4380574567 61 E -7], +--R [1.43,7.0554638,7.0554637664 342109722,- 0.3356578902 78 E -7], +--R [1.44,7.6018261,7.6018260620 257232407,- 0.3797427675 94 E -7], +--R [1.45,8.2380928,8.2380927529 656070833,- 0.4703439291 7 E -7], +--R [1.46,8.9886076,8.9886076017 241695008,0.1724169501 E -8], +--R [1.47,9.8873749,9.8873748919 855531724,- 0.8014446827 5 E -8], +--R [1.48,10.9833793,10.9833793143 26067301,0.1432606730 1 E -7], +--R [1.49,12.3498564,12.3498564416 25802114,0.4162580211 4 E -7], +--R [1.5,14.1014199,14.1014199471 71719388,0.4717171938 8 E -7], +--R [1.51,16.4280917,16.4280917038 85335336,0.3885335336 E -8], +--R [1.52,19.6695278,19.6695278205 58866232,0.2055886623 2 E -7], +--R [1.53,24.4984104,24.4984104418 38034593,0.4183803459 3 E -7], +--R [1.54,32.4611389,32.4611389128 56765176,0.1285676518 E -7], +--R [1.55,48.0784825,48.0784824792 18968279,- 0.2078103172 E -7], +--R [1.56,92.6204963,92.6204963167 04102469,0.1670410247 E -7], +--R [1.57,1255.7655915,1255.7655915006 916051,0.6916051 E -9], +--R [1.58,- 108.6492036,- 108.6492036048 4393447,- 0.484393447 E -8], +--R [1.59,- 52.0669696,- 52.0669696509 12563554,- 0.5091256355 4 E -7], +--R [1.6,- 34.2325327,- 34.2325327355 57417056,- 0.3555741705 7 E -7]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of tan(x), ranging from 0.01 to 1.60. The +second column is the reference value of tan from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp186-188 +<<*>>= + +--S 2 of 2 +[[0.01,99.9966666,cot(0.01),cot(0.01)-(99.9966666)],_ +[0.02,49.9933332,cot(0.02),cot(0.02)-(49.9933332)],_ +[0.03,33.3233327,cot(0.03),cot(0.03)-(33.3233327)],_ +[0.04,24.9866652,cot(0.04),cot(0.04)-(24.9866652)],_ +[0.05,19.9833306,cot(0.05),cot(0.05)-(19.9833306)],_ +[0.06,16.6466619,cot(0.06),cot(0.06)-(16.6466619)],_ +[0.07,14.2623733,cot(0.07),cot(0.07)-(14.2623733)],_ +[0.08,12.4733219,cot(0.08),cot(0.08)-(12.4733219)],_ +[0.09,11.0810949,cot(0.09),cot(0.09)-(11.0810949)],_ +[0.10,9.9666444,cot(0.10),cot(0.10)-(9.9666444)],_ +[0.11,9.0542128,cot(0.11),cot(0.11)-(9.0542128)],_ +[0.12,8.2932949,cot(0.12),cot(0.12)-(8.2932949)],_ +[0.13,7.6489255,cot(0.13),cot(0.13)-(7.6489255)],_ +[0.14,7.0961294,cot(0.14),cot(0.14)-(7.0961294)],_ +[0.15,6.6165915,cot(0.15),cot(0.15)-(6.6165915)],_ +[0.16,6.1965754,cot(0.16),cot(0.16)-(6.1965754)],_ +[0.17,5.8255768,cot(0.17),cot(0.17)-(5.8255768)],_ +[0.18,5.4954256,cot(0.18),cot(0.18)-(5.4954256)],_ +[0.19,5.1996716,cot(0.19),cot(0.19)-(5.1996716)],_ +[0.20,4.9331549,cot(0.20),cot(0.20)-(4.9331549)],_ +[0.21,4.6916981,cot(0.21),cot(0.21)-(4.6916981)],_ +[0.22,4.4718835,cot(0.22),cot(0.22)-(4.4718835)],_ +[0.23,4.2708877,cot(0.23),cot(0.23)-(4.2708877)],_ +[0.24,4.0863578,cot(0.24),cot(0.24)-(4.0863578)],_ +[0.25,3.9163174,cot(0.25),cot(0.25)-(3.9163174)],_ +[0.26,3.7590941,cot(0.26),cot(0.26)-(3.7590941)],_ +[0.27,3.6132632,cot(0.27),cot(0.27)-(3.6132632)],_ +[0.28,3.4776037,cot(0.28),cot(0.28)-(3.4776037)],_ +[0.29,3.3510628,cot(0.29),cot(0.29)-(3.3510628)],_ +[0.30,3.2327281,cot(0.30),cot(0.30)-(3.2327281)],_ +[0.31,3.1218050,cot(0.31),cot(0.31)-(3.1218050)],_ +[0.32,3.0175980,cot(0.32),cot(0.32)-(3.0175980)],_ +[0.33,2.9194961,cot(0.33),cot(0.33)-(2.9194961)],_ +[0.34,2.8269600,cot(0.34),cot(0.34)-(2.8269600)],_ +[0.35,2.7395122,cot(0.35),cot(0.35)-(2.7395122)],_ +[0.36,2.6567280,cot(0.36),cot(0.36)-(2.6567280)],_ +[0.37,2.5782289,cot(0.37),cot(0.37)-(2.5782289)],_ +[0.38,2.5036759,cot(0.38),cot(0.38)-(2.5036759)],_ +[0.39,2.4327650,cot(0.39),cot(0.39)-(2.4327650)],_ +[0.40,2.3652224,cot(0.40),cot(0.40)-(2.3652224)],_ +[0.41,2.3008012,cot(0.41),cot(0.41)-(2.3008012)],_ +[0.42,2.2392778,cot(0.42),cot(0.42)-(2.2392778)],_ +[0.43,2.1804495,cot(0.43),cot(0.43)-(2.1804495)],_ +[0.44,2.1241320,cot(0.44),cot(0.44)-(2.1241320)],_ +[0.45,2.0701574,cot(0.45),cot(0.45)-(2.0701574)],_ +[0.46,2.0183722,cot(0.46),cot(0.46)-(2.0183722)],_ +[0.47,1.9686361,cot(0.47),cot(0.47)-(1.9686361)],_ +[0.48,1.9208205,cot(0.48),cot(0.48)-(1.9208205)],_ +[0.49,1.8748073,cot(0.49),cot(0.49)-(1.8748073)],_ +[0.50,1.83048772,cot(0.50),cot(0.50)-(1.83048772)],_ +[0.51,1.78776154,cot(0.51),cot(0.51)-(1.78776154)],_ +[0.52,1.74653626,cot(0.52),cot(0.52)-(1.74653626)],_ +[0.53,1.70672634,cot(0.53),cot(0.53)-(1.70672634)],_ +[0.54,1.66825255,cot(0.54),cot(0.54)-(1.66825255)],_ +[0.55,1.63104142,cot(0.55),cot(0.55)-(1.63104142)],_ +[0.56,1.59502471,cot(0.56),cot(0.56)-(1.59502471)],_ +[0.57,1.56013894,cot(0.57),cot(0.57)-(1.56013894)],_ +[0.58,1.52632503,cot(0.58),cot(0.58)-(1.52632503)],_ +[0.59,1.49352784,cot(0.59),cot(0.59)-(1.49352784)],_ +[0.60,1.46169595,cot(0.60),cot(0.60)-(1.46169595)],_ +[0.61,1.43078125,cot(0.61),cot(0.61)-(1.43078125)],_ +[0.62,1.40073873,cot(0.62),cot(0.62)-(1.40073873)],_ +[0.63,1.37152626,cot(0.63),cot(0.63)-(1.37152626)],_ +[0.64,1.34310429,cot(0.64),cot(0.64)-(1.34310429)],_ +[0.65,1.31543569,cot(0.65),cot(0.65)-(1.31543569)],_ +[0.66,1.28848559,cot(0.66),cot(0.66)-(1.28848559)],_ +[0.67,1.26222118,cot(0.67),cot(0.67)-(1.26222118)],_ +[0.68,1.23661155,cot(0.68),cot(0.68)-(1.23661155)],_ +[0.69,1.21162759,cot(0.69),cot(0.69)-(1.21162759)],_ +[0.70,1.18724183,cot(0.70),cot(0.70)-(1.18724183)],_ +[0.71,1.16342833,cot(0.71),cot(0.71)-(1.16342833)],_ +[0.72,1.14016258,cot(0.72),cot(0.72)-(1.14016258)],_ +[0.73,1.11742140,cot(0.73),cot(0.73)-(1.11742140)],_ +[0.74,1.09518285,cot(0.74),cot(0.74)-(1.09518285)],_ +[0.75,1.07342615,cot(0.75),cot(0.75)-(1.07342615)],_ +[0.76,1.05213158,cot(0.76),cot(0.76)-(1.05213158)],_ +[0.77,1.03128046,cot(0.77),cot(0.77)-(1.03128046)],_ +[0.78,1.01085503,cot(0.78),cot(0.78)-(1.01085503)],_ +[0.79,0.99083842,cot(0.79),cot(0.79)-(0.99083842)],_ +[0.80,0.97121460,cot(0.80),cot(0.80)-(0.97121460)],_ +[0.81,0.95196830,cot(0.81),cot(0.81)-(0.95196830)],_ +[0.82,0.93308500,cot(0.82),cot(0.82)-(0.93308500)],_ +[0.83,0.91455085,cot(0.83),cot(0.83)-(0.91455085)],_ +[0.84,0.89635264,cot(0.84),cot(0.84)-(0.89635264)],_ +[0.85,0.87847778,cot(0.85),cot(0.85)-(0.87847778)],_ +[0.86,0.86091426,cot(0.86),cot(0.86)-(0.86091426)],_ +[0.87,0.84365058,cot(0.87),cot(0.87)-(0.84365058)],_ +[0.88,0.82667575,cot(0.88),cot(0.88)-(0.82667575)],_ +[0.89,0.80997930,cot(0.89),cot(0.89)-(0.80997930)],_ +[0.90,0.79355115,cot(0.90),cot(0.90)-(0.79355115)],_ +[0.91,0.77738169,cot(0.91),cot(0.91)-(0.77738169)],_ +[0.92,0.76146169,cot(0.92),cot(0.92)-(0.76146169)],_ +[0.93,0.74578232,cot(0.93),cot(0.93)-(0.74578232)],_ +[0.94,0.73033510,cot(0.94),cot(0.94)-(0.73033510)],_ +[0.95,0.71511188,cot(0.95),cot(0.95)-(0.71511188)],_ +[0.96,0.70010485,cot(0.96),cot(0.96)-(0.70010485)],_ +[0.97,0.68530649,cot(0.97),cot(0.97)-(0.68530649)],_ +[0.98,0.67070959,cot(0.98),cot(0.98)-(0.67070959)],_ +[0.99,0.65630719,cot(0.99),cot(0.99)-(0.65630719)],_ +[1.00,0.64209262,cot(1.00),cot(1.00)-(0.64209262)],_ +[1.01,0.62805942,cot(1.01),cot(1.01)-(0.62805942)],_ +[1.02,0.61420141,cot(1.02),cot(1.02)-(0.61420141)],_ +[1.03,0.60051260,cot(1.03),cot(1.03)-(0.60051260)],_ +[1.04,0.58698722,cot(1.04),cot(1.04)-(0.58698722)],_ +[1.05,0.57361970,cot(1.05),cot(1.05)-(0.57361970)],_ +[1.06,0.56040467,cot(1.06),cot(1.06)-(0.56040467)],_ +[1.07,0.54733693,cot(1.07),cot(1.07)-(0.54733693)],_ +[1.08,0.53441147,cot(1.08),cot(1.08)-(0.53441147)],_ +[1.09,0.52162342,cot(1.09),cot(1.09)-(0.52162342)],_ +[1.10,0.50896811,cot(1.10),cot(1.10)-(0.50896811)],_ +[1.11,0.49644096,cot(1.11),cot(1.11)-(0.49644096)],_ +[1.12,0.48403759,cot(1.12),cot(1.12)-(0.48403759)],_ +[1.13,0.47175371,cot(1.13),cot(1.13)-(0.47175371)],_ +[1.14,0.45958520,cot(1.14),cot(1.14)-(0.45958520)],_ +[1.15,0.44752802,cot(1.15),cot(1.15)-(0.44752802)],_ +[1.16,0.43557829,cot(1.16),cot(1.16)-(0.43557829)],_ +[1.17,0.42373221,cot(1.17),cot(1.17)-(0.42373221)],_ +[1.18,0.41198610,cot(1.18),cot(1.18)-(0.41198610)],_ +[1.19,0.40033638,cot(1.19),cot(1.19)-(0.40033638)],_ +[1.20,0.38877957,cot(1.20),cot(1.20)-(0.38877957)],_ +[1.21,0.37731227,cot(1.21),cot(1.21)-(0.37731227)],_ +[1.22,0.36593119,cot(1.22),cot(1.22)-(0.36593119)],_ +[1.23,0.35463310,cot(1.23),cot(1.23)-(0.35463310)],_ +[1.24,0.34341486,cot(1.24),cot(1.24)-(0.34341486)],_ +[1.25,0.33227342,cot(1.25),cot(1.25)-(0.33227342)],_ +[1.26,0.32120577,cot(1.26),cot(1.26)-(0.32120577)],_ +[1.27,0.31020899,cot(1.27),cot(1.27)-(0.31020899)],_ +[1.28,0.29928023,cot(1.28),cot(1.28)-(0.29928023)],_ +[1.29,0.28841670,cot(1.29),cot(1.29)-(0.28841670)],_ +[1.30,0.27761565,cot(1.30),cot(1.30)-(0.27761565)],_ +[1.31,0.26687440,cot(1.31),cot(1.31)-(0.26687440)],_ +[1.32,0.25619034,cot(1.32),cot(1.32)-(0.25619034)],_ +[1.33,0.24556088,cot(1.33),cot(1.33)-(0.24556088)],_ +[1.34,0.23498350,cot(1.34),cot(1.34)-(0.23498350)],_ +[1.35,0.22445572,cot(1.35),cot(1.35)-(0.22445572)],_ +[1.36,0.21397509,cot(1.36),cot(1.36)-(0.21397509)],_ +[1.37,0.20353922,cot(1.37),cot(1.37)-(0.20353922)],_ +[1.38,0.19314574,cot(1.38),cot(1.38)-(0.19314574)],_ +[1.39,0.18279234,cot(1.39),cot(1.39)-(0.18279234)],_ +[1.40,0.17247673,cot(1.40),cot(1.40)-(0.17247673)],_ +[1.41,0.16219663,cot(1.41),cot(1.41)-(0.16219663)],_ +[1.42,0.15194983,cot(1.42),cot(1.42)-(0.15194983)],_ +[1.43,0.14173413,cot(1.43),cot(1.43)-(0.14173413)],_ +[1.44,0.13154734,cot(1.44),cot(1.44)-(0.13154734)],_ +[1.45,0.12138732,cot(1.45),cot(1.45)-(0.12138732)],_ +[1.46,0.11125194,cot(1.46),cot(1.46)-(0.11125194)],_ +[1.47,0.10113908,cot(1.47),cot(1.47)-(0.10113908)],_ +[1.48,0.091046660,cot(1.48),cot(1.48)-(0.091046660)],_ +[1.49,0.080972601,cot(1.49),cot(1.49)-(0.080972601)],_ +[1.50,0.070914844,cot(1.50),cot(1.50)-(0.070914844)],_ +[1.51,0.060871343,cot(1.51),cot(1.51)-(0.060871343)],_ +[1.52,0.050840061,cot(1.52),cot(1.52)-(0.050840061)],_ +[1.53,0.040818975,cot(1.53),cot(1.53)-(0.040818975)],_ +[1.54,0.030806066,cot(1.54),cot(1.54)-(0.030806066)],_ +[1.55,0.020799325,cot(1.55),cot(1.55)-(0.020799325)],_ +[1.56,0.010796746,cot(1.56),cot(1.56)-(0.010796746)],_ +[1.57,0.000796327,cot(1.57),cot(1.57)-(0.000796327)],_ +[1.58,-0.009203933,cot(1.58),cot(1.58)-(-0.009203933)],_ +[1.59,-0.019206034,cot(1.59),cot(1.59)-(-0.019206034)],_ +[1.60,-0.029211978,cot(1.60),cot(1.60)-(-0.029211978)]] +--R +--R +--R (2) +--R [[0.01,99.9966666,99.9966666444 44232802,0.444442328 E -7], +--R [0.02,49.9933332,49.9933331555 48782798,- 0.4445121720 2 E -7], +--R [0.03,33.3233327,33.3233327332 81900133,0.3328190013 3 E -7], +--R [0.04,24.9866652,24.9866652442 27690187,0.4422769018 7 E -7], +--R [0.05,19.9833306,19.9833305548 94014508,- 0.4510598549 1 E -7], +--R [0.06,16.6466619,16.6466618650 20359708,- 0.3497964029 2 E -7], +--R [0.07,14.2623733,14.2623733265 9994931,0.2659994931 E -7], +--R [0.08,12.4733219,12.4733219486 16087812,0.4861608781 2 E -7], +--R [0.09,11.0810949,11.0810948986 03837279,- 0.1396162721 E -8], +--R [0.1,9.9666444,9.9666444232 592378598,0.2325923786 E -7], +--R [0.11,9.0542128,9.0542128123 384855803,0.1233848558 E -7], +--R [0.12,8.2932949,8.2932948805 945312103,- 0.1940546879 E -7], +--R [0.13,7.6489255,7.6489254580 38579468,- 0.4196142053 2 E -7], +--R [0.14,7.0961294,7.0961293843 639732986,- 0.1563602670 1 E -7], +--R [0.15,6.6165915,6.6165915055 899500987,0.5589950098 7 E -8], +--R [0.16,6.1965754,6.1965754219 540076277,0.2195400762 8 E -7], +--R [0.17,5.8255768,5.8255767953 622059416,- 0.4637794058 4 E -8], +--R [0.18,5.4954256,5.4954255543 470259144,- 0.4565297408 56 E -7], +--R [0.19,5.1996716,5.1996716132 404544488,0.1324045444 9 E -7], +--R [0.2,4.9331549,4.9331548755 868936573,- 0.2441310634 3 E -7], +--R [0.21,4.6916981,4.6916980937 15878191,- 0.6284121809 E -8], +--R [0.22,4.4718835,4.4718834938 782225379,- 0.6121777462 1 E -8], +--R [0.23,4.2708877,4.2708876730 783907862,- 0.2692160921 4 E -7], +--R [0.24,4.0863578,4.0863577716 916129493,- 0.2830838705 1 E -7], +--R [0.25,3.9163174,3.9163173646 45940105,- 0.3535405989 5 E -7], +--R [0.26,3.7590941,3.7590940700 170597097,- 0.2998294029 03 E -7], +--R [0.27,3.6132632,3.6132632445 954451122,0.4459544511 22 E -7], +--R [0.28,3.4776037,3.4776037446 826739597,0.4468267395 97 E -7], +--R [0.29,3.3510628,3.3510628398 201367735,0.3982013677 35 E -7], +--R [0.3,3.2327281,3.2327281437 658275137,0.4376582751 37 E -7], +--R [0.31,3.121805,3.1218049781 792418003,- 0.2182075819 97 E -7], +--R [0.32,3.017598,3.0175979806 093983387,- 0.1939060166 13 E -7], +--R [0.33,2.9194961,2.9194960564 791734711,- 0.4352082652 89 E -7], +--R [0.34,2.82696,2.8269599865 960316187,- 0.1340396838 1 E -7], +--R [0.35,2.7395122,2.7395121590 837832657,- 0.4091621673 43 E -7], +--R [0.36,2.656728,2.6567280126 534137138,0.1265341371 4 E -7], +--R [0.37,2.5782289,2.5782288674 460399215,- 0.3255396007 85 E -7], +--R [0.38,2.5036759,2.5036758878 425107672,- 0.1215748923 3 E -7], +--R [0.39,2.432765,2.4327649740 660567805,- 0.2593394321 95 E -7], +--R [0.4,2.3652224,2.3652224200 39110587,0.2003911058 7 E -7], +--R [0.41,2.3008012,2.3008012066 70318891,0.6670318891 E -8], +--R [0.42,2.2392778,2.2392778246 666163969,0.2466661639 69 E -7], +--R [0.43,2.1804495,2.1804495406 685083798,0.4066850837 98 E -7], +--R [0.44,2.124132,2.1241320361 797692227,0.3617976922 27 E -7], +--R [0.45,2.0701574,2.0701573613 012126215,- 0.3869878737 85 E -7], +--R [0.46,2.0183722,2.0183721553 634627578,- 0.4463653724 22 E -7], +--R [0.47,1.9686361,1.9686360947 077066311,- 0.5292293368 9 E -8], +--R [0.48,1.9208205,1.9208205344 885739853,0.3448857398 53 E -7], +--R [0.49,1.8748073,1.8748073167 815901303,0.1678159013 03 E -7], +--R [0.5,1.83048772,1.8304877217 124519193,0.1712451919 3 E -8], +--R [0.51,1.78776154,1.7877615419 775693505,0.1977569350 5 E -8], +--R [0.52,1.74653626,1.7465362641 453971653,0.4145397165 3 E -8], +--R [0.53,1.70672634,1.7067263426 353184999,0.2635318499 9 E -8], +--R [0.54,1.66825255,1.6682525543 602072732,0.4360207273 2 E -8], +--R [0.55,1.63104142,1.6310414237 662644566,0.3766264456 6 E -8], +--R [0.56,1.59502471,1.5950247094 703485723,- 0.5296514276 E -9], +--R [0.57,1.56013894,1.5601389449 30073432,0.4930073431 9 E -8], +--R [0.58,1.52632503,1.5263250266 253525611,- 0.3374647438 9 E -8], +--R [0.59,1.49352784,1.4935278441 14312362,0.4114312362 E -8], +--R [0.6,1.46169595,1.4616959470 781021403,- 0.2921897859 7 E -8], +--R [0.61,1.43078125,1.4307812451 098423602,- 0.4890157639 8 E -8], +--R [0.62,1.40073873,1.4007387365 5065882,0.655065882 E -8], +--R [0.63,1.37152626,1.3715262631 452128637,0.3145212863 7 E -8], +--R [0.64,1.34310429,1.3431042876 925818576,- 0.2307418142 4 E -8], +--R [0.65,1.31543569,1.3154356922 15926629,0.2215926629 E -8], +--R [0.66,1.28848559,1.2884855944 745672615,0.4474567261 5 E -8], +--R [0.67,1.26222118,1.2622211809 019498574,0.9019498574 E -9], +--R [0.68,1.23661155,1.2366115542 784545265,0.4278454526 5 E -8], +--R [0.69,1.21162759,1.2116275946 440535197,0.4644053519 7 E -8], +--R [0.7,1.18724183,1.1872418321 266793537,0.2126679353 7 E -8], +--R [0.71,1.16342833,1.1634283305 113563708,0.5113563708 E -9], +--R [0.72,1.14016258,1.1401625805 056933781,0.5056933781 E -9], +--R [0.73,1.1174214,1.1174214017 717845341,0.1771784534 1 E -8], +--R [0.74,1.09518285,1.0951828528 950954346,0.2895095434 6 E -8], +--R [0.75,1.07342615,1.0734261485 493773587,- 0.1450622641 3 E -8], +--R [0.76,1.05213158,1.0521315831 946421944,0.3194642194 4 E -8], +--R [0.77,1.03128046,1.0312804607 141042446,0.7141042446 E -9], +--R [0.78,1.01085503,1.0108550294 569216086,- 0.5430783914 E -9], +--R [0.79,0.99083842,0.9908384222 0755510722,0.2207555107 2 E -8], +--R [0.8,0.9712146,0.9712146006 5047441252,0.6504744125 2 E -9], +--R [0.81,0.9519683,0.9519683039 4152897039,0.3941528970 39 E -8], +--R [0.82,0.933085,0.9330850010 3521469901,0.1035214699 E -8], +--R [0.83,0.91455085,0.9145508464 5086948692,- 0.3549130513 1 E -8], +--R [0.84,0.89635264,0.8963526391 9101064443,- 0.8089893555 7 E -9], +--R [0.85,0.87847778,0.8784777845 5201177212,0.4552011772 12 E -8], +--R [0.86,0.86091426,0.8609142585 9147659674,- 0.1408523403 3 E -8], +--R [0.87,0.84365058,0.8436505750 3832779908,- 0.4961672200 92 E -8], +--R [0.88,0.82667575,0.8266757544 5107375391,0.4451073753 91 E -8], +--R [0.89,0.8099793,0.8099792954 4719434615,- 0.4552805653 85 E -8], +--R [0.9,0.79355115,0.7935511478 423171255,- 0.2157682874 5 E -8], +--R [0.91,0.77738169,0.7773816875 5202909939,- 0.2447970900 6 E -8], +--R [0.92,0.76146169,0.7614616931 2195656768,0.3121956567 7 E -8], +--R [0.93,0.74578232,0.7457823237 6329468591,0.3763294685 91 E -8], +--R [0.94,0.7303351,0.7303350987 8141157551,- 0.1218588424 5 E -8], +--R [0.95,0.71511188,0.7151118782 9460519926,- 0.1705394800 7 E -8], +--R [0.96,0.70010485,0.7001048451 4865796784,- 0.4851342032 16 E -8], +--R [0.97,0.68530649,0.6853064879 4060552823,- 0.2059394471 8 E -8], +--R [0.98,0.67070959,0.6707095850 721935367,- 0.4927806463 3 E -8], +--R [0.99,0.65630719,0.6563071897 5991155454,- 0.2400884455 E -9], +--R [1.0,0.64209262,0.6420926159 3433070301,- 0.4065669296 99 E -8], +--R [1.01,0.62805942,0.6280594249 6678856739,0.4966788567 39 E -8], +--R [1.02,0.61420141,0.6142014131 6631206854,0.3166312068 5 E -8], +--R [1.03,0.6005126,0.6005125999 9409219665,- 0.590780335 E -11], +--R [1.04,0.58698722,0.5869872169 4686437526,- 0.3053135624 7 E -8], +--R [1.05,0.5736197,0.5736196970 6424127541,- 0.2935758724 6 E -8], +--R [1.06,0.56040467,0.5604046650 184238209,- 0.4981576179 09 E -8], +--R [1.07,0.54733693,0.5473369277 478102494,- 0.2252189750 6 E -8], +--R [1.08,0.53441147,0.5344114655 9885875935,- 0.4401141240 65 E -8], +--R [1.09,0.52162342,0.5216234239 4316016472,0.3943160164 72 E -8], +--R [1.1,0.50896811,0.5089681052 3906440719,- 0.4760935592 81 E -8], +--R [1.11,0.49644096,0.4964409615 0939793968,0.1509397939 7 E -8], +--R [1.12,0.48403759,0.4840375872 0882520651,- 0.2791174793 49 E -8], +--R [1.13,0.47175371,0.4717537124 562623272,0.2456262327 2 E -8], +--R [1.14,0.4595852,0.4595851966 0945875941,- 0.3390541240 59 E -8], +--R [1.15,0.44752802,0.4475280221 6043593272,0.2160435932 72 E -8], +--R [1.16,0.43557829,0.4355782889 3192216044,- 0.1068077839 6 E -8], +--R [1.17,0.42373221,0.4237322085 562610121,- 0.1443738987 9 E -8], +--R [1.18,0.4119861,0.4119860992 1950525045,- 0.7804947495 5 E -9], +--R [1.19,0.40033638,0.4003363806 5454900775,0.6545490077 5 E -9], +--R [1.2,0.38877957,0.3887795693 6820491163,- 0.6317950883 7 E -9], +--R [1.21,0.37731227,0.3773122740 8810747104,0.4088107471 05 E -8], +--R [1.22,0.36593119,0.3659311914 1622565487,0.1416225654 9 E -8], +--R [1.23,0.3546331,0.3546331016 7660211852,0.1676602118 5 E -8], +--R [1.24,0.34341486,0.3434148649 4570930705,0.4945709307 05 E -8], +--R [1.25,0.33227342,0.3322734172 5452856774,- 0.2745471432 26 E -8], +--R [1.26,0.32120577,0.3212057669 5212188699,- 0.3047878113 01 E -8], +--R [1.27,0.31020899,0.3102089912 2108098744,0.1221080987 4 E -8], +--R [1.28,0.29928023,0.2992802327 358089858,0.2735808985 8 E -8], +--R [1.29,0.2884167,0.2884166964 5511900872,- 0.3544880991 28 E -8], +--R [1.3,0.27761565,0.2776156465 411251863,- 0.3458874813 7 E -8], +--R [1.31,0.2668744,0.2668744033 9685712292,0.3396857122 92 E -8], +--R [1.32,0.25619034,0.2561903408 1545187187,0.8154518718 7 E -9], +--R [1.33,0.24556088,0.2455608832 341699844,0.3234169984 4 E -8], +--R [1.34,0.2349835,0.2349835030 8684653553,0.3086846535 53 E -8], +--R [1.35,0.22445572,0.2244557182 4872613589,- 0.1751273864 11 E -8], +--R [1.36,0.21397509,0.2139750895 6794464051,- 0.4320553594 9 E -9], +--R [1.37,0.20353922,0.2035392184 7821123118,- 0.1521788768 82 E -8], +--R [1.38,0.19314574,0.1931457446 8751430396,0.4687514303 96 E -8], +--R [1.39,0.18279234,0.1827923439 3792453991,0.3937924539 91 E -8], +--R [1.4,0.17247673,0.1724767258 3179995277,- 0.4168200047 23 E -8], +--R [1.41,0.16219663,0.1621966317 1991176955,0.1719911769 56 E -8], +--R [1.42,0.15194983,0.1519498326 4720777741,0.2647207777 41 E -8], +--R [1.43,0.14173413,0.1417341273 5211224764,- 0.2647887752 36 E -8], +--R [1.44,0.13154734,0.1315473403 1542961869,0.3154296186 9 E -9], +--R [1.45,0.12138732,0.1213873198 5507360359,- 0.1449263964 1 E -9], +--R [1.46,0.11125194,0.1112519362 6298502613,- 0.3737014973 87 E -8], +--R [1.47,0.10113908,0.1011390799 8073116239,- 0.1926883761 E -10], +--R [1.48,0.09104666,0.0910466598 1039728128,- 0.1896027187 2 E -9], +--R [1.49,0.080972601,0.0809726011 5748799537,0.1574879953 7 E -9], +--R [1.5,0.070914844,0.0709148443 0265244878 9,0.3026524487 9 E -9], +--R [1.51,0.060871343,0.0608713426 9913372964 9,- 0.3008662703 51 E -9], +--R [1.52,0.050840061,0.0508400612 9291959823 6,0.2929195982 36 E -9], +--R [1.53,0.040818975,0.0408189748 6263901912 7,- 0.1373609808 7 E -9], +--R [1.54,0.030806066,0.0308060663 7630738330 6,0.3763073833 07 E -9], +--R [1.55,0.020799325,0.0207993253 6207296975 6,0.3620729697 56 E -9], +--R [1.56,0.010796746,0.0107967462 901583485,0.2901583485 E -9], +--R [1.57,0.000796327,0.0007963269 6322325475 679,- 0.3677674524 32 E -10], +--R [1.58,- 0.009203933,- 0.0092039330 8759988693 76,- 0.8759988693 75 E -10], +--R [1.59,- 0.019206034,- 0.0192060342 0373002777 9,- 0.2037300277 79 E -9], +--R [1.6,- 0.029211978,- 0.0292119781 9994480011 4,- 0.1999448001 14 E -9]] +--R Type: List List Float +--E 2 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp186-188 +\end{thebibliography} +\end{document} + diff --git a/src/input/tanhcoth.input.pamphlet b/src/input/tanhcoth.input.pamphlet new file mode 100644 index 0000000..c076ef9 --- /dev/null +++ b/src/input/tanhcoth.input.pamphlet @@ -0,0 +1,860 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input tanhcoth.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is a set of tests for the tanh and coth functions. +\end{abstract} +\eject +\tableofcontents +\eject +In the following table there are 4 columns. The first column +is the argument of tanh, ranging from 0.00 to 2.00. The +second column is the reference value of tanh from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp213-216 + +<<*>>= +)spool tanhcoth.output +)set message test on +)set message auto off +)clear all + +--S 1 of 2 +[[0.00,0.00000000,tanh(0.00),tanh(0.00)-0.00000000],_ +[0.01,0.00999967,tanh(0.01),tanh(0.01)-0.00999967],_ +[0.02,0.01999733,tanh(0.02),tanh(0.02)-0.01999733],_ +[0.03,0.02999100,tanh(0.03),tanh(0.03)-0.02999100],_ +[0.04,0.03997868,tanh(0.04),tanh(0.04)-0.03997868],_ +[0.05,0.04995838,tanh(0.05),tanh(0.05)-0.04995838],_ +[0.06,0.05992810,tanh(0.06),tanh(0.06)-0.05992810],_ +[0.07,0.06988589,tanh(0.07),tanh(0.07)-0.06988589],_ +[0.08,0.07982977,tanh(0.08),tanh(0.08)-0.07982977],_ +[0.09,0.08975779,tanh(0.09),tanh(0.09)-0.08975779],_ +[0.10,0.09966800,tanh(0.10),tanh(0.10)-0.09966800],_ +[0.11,0.10955847,tanh(0.11),tanh(0.11)-0.10955847],_ +[0.12,0.11942730,tanh(0.12),tanh(0.12)-0.11942730],_ +[0.13,0.12927258,tanh(0.13),tanh(0.13)-0.12927258],_ +[0.14,0.13909245,tanh(0.14),tanh(0.14)-0.13909245],_ +[0.15,0.14888503,tanh(0.15),tanh(0.15)-0.14888503],_ 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+--R [1.99,0.96331422,0.9633142186 0451342618,- 0.1395486573 8 E -8], +--R [2.0,0.96402758,0.9640275800 7581688395,0.7581688395 E -10]] +--R Type: List List Float +--E 1 +@ +In the following table there are 4 columns. The first column +is the argument of coth, ranging from 0.01 to 2.00. The +second column is the reference value of coth from the book +Abramowitz and Stegun, ``Handbook of Mathematical Functions'', +Dover Publications, Inc. New York 1965. pp213-216 + +<<*>>= +--S 2 of 2 +[[0.01,100.0033333,coth(0.01),coth(0.01)-100.003333],_ +[0.02,50.0066665,coth(0.02),coth(0.02)-50.0066665],_ +[0.03,33.3433327,coth(0.03),coth(0.03)-33.3433327],_ +[0.04,25.0133319,coth(0.04),coth(0.04)-25.0133319],_ +[0.05,20.0166639,coth(0.05),coth(0.05)-20.0166639],_ +[0.06,16.6866619,coth(0.06),coth(0.06)-16.6866619],_ +[0.07,14.3090400,coth(0.07),coth(0.07)-14.3090400],_ +[0.08,12.5266553,coth(0.08),coth(0.08)-12.5266553],_ +[0.09,11.1410949,coth(0.09),coth(0.09)-11.1410949],_ +[0.10,10.0333111,coth(0.10),coth(0.10)-10.0333111],_ +[0.11,9.1275462,coth(0.11),coth(0.11)-9.1275462],_ +[0.12,8.3732950,coth(0.12),coth(0.12)-8.3732950],_ +[0.13,7.7355923,coth(0.13),coth(0.13)-7.7355923],_ +[0.14,7.1894629,coth(0.14),coth(0.14)-7.1894629],_ +[0.15,6.7165918,coth(0.15),coth(0.15)-6.7165918],_ +[0.16,6.3032425,coth(0.16),coth(0.16)-6.3032425],_ +[0.17,5.9389107,coth(0.17),coth(0.17)-5.9389107],_ +[0.18,5.6154264,coth(0.18),coth(0.18)-5.6154264],_ +[0.19,5.3263393,coth(0.19),coth(0.19)-5.3263393],_ +[0.20,5.0664896,coth(0.20),coth(0.20)-5.0664896],_ +[0.21,4.8316998,coth(0.21),coth(0.21)-4.8316998],_ +[0.22,4.6185523,coth(0.22),coth(0.22)-4.6185523],_ +[0.23,4.4242237,coth(0.23),coth(0.23)-4.4242237],_ +[0.24,4.2463611,coth(0.24),coth(0.24)-4.2463611],_ +[0.25,4.0829882,coth(0.25),coth(0.25)-4.0829882],_ +[0.26,3.9324324,coth(0.26),coth(0.26)-3.9324324],_ +[0.27,3.7932693,coth(0.27),coth(0.27)-3.7932693],_ +[0.28,3.6642777,coth(0.28),coth(0.28)-3.6642777],_ +[0.29,3.5444049,coth(0.29),coth(0.29)-3.5444049],_ +[0.30,3.4327384,coth(0.30),coth(0.30)-3.4327384],_ +[0.31,3.3284838,coth(0.31),coth(0.31)-3.3284838],_ +[0.32,3.2309455,coth(0.32),coth(0.32)-3.2309455],_ +[0.33,3.1395126,coth(0.33),coth(0.33)-3.1395126],_ +[0.34,3.0536459,coth(0.34),coth(0.34)-3.0536459],_ +[0.35,2.9728677,coth(0.35),coth(0.35)-2.9728677],_ +[0.36,2.8967536,coth(0.36),coth(0.36)-2.8967536],_ +[0.37,2.8249249,coth(0.37),coth(0.37)-2.8249249],_ +[0.38,2.7570428,coth(0.38),coth(0.38)-2.7570428],_ +[0.39,2.6928032,coth(0.39),coth(0.39)-2.6928032],_ +[0.40,2.6319324,coth(0.40),coth(0.40)-2.6319324],_ +[0.41,2.5741836,coth(0.41),coth(0.41)-2.5741836],_ +[0.42,2.5193332,coth(0.42),coth(0.42)-2.5193332],_ +[0.43,2.4671785,coth(0.43),coth(0.43)-2.4671785],_ +[0.44,2.4175352,coth(0.44),coth(0.44)-2.4175352],_ +[0.45,2.3702355,coth(0.45),coth(0.45)-2.3702355],_ +[0.46,2.3251260,coth(0.46),coth(0.46)-2.3251260],_ +[0.47,2.2820666,coth(0.47),coth(0.47)-2.2820666],_ +[0.48,2.2409284,coth(0.48),coth(0.48)-2.2409284],_ +[0.49,2.2015936,coth(0.49),coth(0.49)-2.2015936],_ +[0.50,2.1639534,coth(0.50),coth(0.50)-2.1639534],_ +[0.51,2.1279077,coth(0.51),coth(0.51)-2.1279077],_ +[0.52,2.0933640,coth(0.52),coth(0.52)-2.0933640],_ +[0.53,2.0602368,coth(0.53),coth(0.53)-2.0602368],_ +[0.54,2.0284471,coth(0.54),coth(0.54)-2.0284471],_ +[0.55,1.9979213,coth(0.55),coth(0.55)-1.9979213],_ +[0.56,1.9685914,coth(0.56),coth(0.56)-1.9685914],_ +[0.57,1.9403939,coth(0.57),coth(0.57)-1.9403939],_ +[0.58,1.9132698,coth(0.58),coth(0.58)-1.9132698],_ +[0.59,1.8871642,coth(0.59),coth(0.59)-1.8871642],_ +[0.60,1.8620255,coth(0.60),coth(0.60)-1.8620255],_ +[0.61,1.8378059,coth(0.61),coth(0.61)-1.8378059],_ +[0.62,1.8144604,coth(0.62),coth(0.62)-1.8144604],_ +[0.63,1.7919470,coth(0.63),coth(0.63)-1.7919470],_ +[0.64,1.7702262,coth(0.64),coth(0.64)-1.7702262],_ +[0.65,1.7492610,coth(0.65),coth(0.65)-1.7492610],_ +[0.66,1.7290167,coth(0.66),coth(0.66)-1.7290167],_ +[0.67,1.7094605,coth(0.67),coth(0.67)-1.7094605],_ +[0.68,1.6905616,coth(0.68),coth(0.68)-1.6905616],_ +[0.69,1.6722911,coth(0.69),coth(0.69)-1.6722911],_ +[0.70,1.6546216,coth(0.70),coth(0.70)-1.6546216],_ +[0.71,1.6375273,coth(0.71),coth(0.71)-1.6375273],_ +[0.72,1.6209838,coth(0.72),coth(0.72)-1.6209838],_ +[0.73,1.6049681,coth(0.73),coth(0.73)-1.6049681],_ +[0.74,1.5894583,coth(0.74),coth(0.74)-1.5894583],_ +[0.75,1.5744338,coth(0.75),coth(0.75)-1.5744338],_ +[0.76,1.5598751,coth(0.76),coth(0.76)-1.5598751],_ +[0.77,1.5457636,coth(0.77),coth(0.77)-1.5457636],_ +[0.78,1.5320817,coth(0.78),coth(0.78)-1.5320817],_ +[0.79,1.5188127,coth(0.79),coth(0.79)-1.5188127],_ +[0.80,1.5059407,coth(0.80),coth(0.80)-1.5059407],_ +[0.81,1.4934506,coth(0.81),coth(0.81)-1.4934506],_ +[0.82,1.4813281,coth(0.82),coth(0.82)-1.4813281],_ +[0.83,1.4695595,coth(0.83),coth(0.83)-1.4695595],_ +[0.84,1.4581318,coth(0.84),coth(0.84)-1.4581318],_ +[0.85,1.4470325,coth(0.85),coth(0.85)-1.4470325],_ +[0.86,1.4362499,coth(0.86),coth(0.86)-1.4362499],_ +[0.87,1.4257726,coth(0.87),coth(0.87)-1.4257726],_ +[0.88,1.4155898,coth(0.88),coth(0.88)-1.4155898],_ +[0.89,1.4056913,coth(0.89),coth(0.89)-1.4056913],_ +[0.90,1.3960673,coth(0.90),coth(0.90)-1.3960673],_ +[0.91,1.3867082,coth(0.91),coth(0.91)-1.3867082],_ +[0.92,1.3776051,coth(0.92),coth(0.92)-1.3776051],_ +[0.93,1.3687495,coth(0.93),coth(0.93)-1.3687495],_ +[0.94,1.3601329,coth(0.94),coth(0.94)-1.3601329],_ +[0.95,1.3517476,coth(0.95),coth(0.95)-1.3517476],_ +[0.96,1.3435860,coth(0.96),coth(0.96)-1.3435860],_ +[0.97,1.3356408,coth(0.97),coth(0.97)-1.3356408],_ +[0.98,1.3279050,coth(0.98),coth(0.98)-1.3279050],_ +[0.99,1.3203720,coth(0.99),coth(0.99)-1.3203720],_ +[1.00,1.3130353,coth(1.00),coth(1.00)-1.3130353],_ +[1.01,1.3058887,coth(1.01),coth(1.01)-1.3058887],_ +[1.02,1.2989264,coth(1.02),coth(1.02)-1.2989264],_ +[1.03,1.2921427,coth(1.03),coth(1.03)-1.2921427],_ +[1.04,1.2855320,coth(1.04),coth(1.04)-1.2855320],_ +[1.05,1.2790891,coth(1.05),coth(1.05)-1.2790891],_ +[1.06,1.2728090,coth(1.06),coth(1.06)-1.2728090],_ +[1.07,1.2666867,coth(1.07),coth(1.07)-1.2666867],_ +[1.08,1.2607175,coth(1.08),coth(1.08)-1.2607175],_ +[1.09,1.2548970,coth(1.09),coth(1.09)-1.2548970],_ +[1.10,1.2492208,coth(1.10),coth(1.10)-1.2492208],_ +[1.11,1.2436846,coth(1.11),coth(1.11)-1.2436846],_ +[1.12,1.2382844,coth(1.12),coth(1.12)-1.2382844],_ +[1.13,1.2330163,coth(1.13),coth(1.13)-1.2330163],_ +[1.14,1.2278766,coth(1.14),coth(1.14)-1.2278766],_ +[1.15,1.2228615,coth(1.15),coth(1.15)-1.2228615],_ +[1.16,1.2179676,coth(1.16),coth(1.16)-1.2179676],_ +[1.17,1.2131915,coth(1.17),coth(1.17)-1.2131915],_ +[1.18,1.2085299,coth(1.18),coth(1.18)-1.2085299],_ +[1.19,1.2039796,coth(1.19),coth(1.19)-1.2039796],_ +[1.20,1.1995375,coth(1.20),coth(1.20)-1.1995375],_ +[1.21,1.1952008,coth(1.21),coth(1.21)-1.1952008],_ +[1.22,1.1909665,coth(1.22),coth(1.22)-1.1909665],_ +[1.23,1.1868319,coth(1.23),coth(1.23)-1.1868319],_ +[1.24,1.1827942,coth(1.24),coth(1.24)-1.1827942],_ +[1.25,1.1788510,coth(1.25),coth(1.25)-1.1788510],_ +[1.26,1.1749996,coth(1.26),coth(1.26)-1.1749996],_ +[1.27,1.1712377,coth(1.27),coth(1.27)-1.1712377],_ +[1.28,1.1675629,coth(1.28),coth(1.28)-1.1675629],_ +[1.29,1.1639729,coth(1.29),coth(1.29)-1.1639729],_ +[1.30,1.1604655,coth(1.30),coth(1.30)-1.1604655],_ +[1.31,1.1570386,coth(1.31),coth(1.31)-1.1570386],_ +[1.32,1.1536901,coth(1.32),coth(1.32)-1.1536901],_ +[1.33,1.1504179,coth(1.33),coth(1.33)-1.1504179],_ +[1.34,1.1472202,coth(1.34),coth(1.34)-1.1472202],_ +[1.35,1.1440950,coth(1.35),coth(1.35)-1.1440950],_ +[1.36,1.1410405,coth(1.36),coth(1.36)-1.1410405],_ +[1.37,1.1380550,coth(1.37),coth(1.37)-1.1380550],_ +[1.38,1.1351366,coth(1.38),coth(1.38)-1.1351366],_ +[1.39,1.1322837,coth(1.39),coth(1.39)-1.1322837],_ +[1.40,1.1294947,coth(1.40),coth(1.40)-1.1294947],_ +[1.41,1.1267680,coth(1.41),coth(1.41)-1.1267680],_ +[1.42,1.1241021,coth(1.42),coth(1.42)-1.1241021],_ +[1.43,1.1214954,coth(1.43),coth(1.43)-1.1214954],_ +[1.44,1.1189466,coth(1.44),coth(1.44)-1.1189466],_ +[1.45,1.1164541,coth(1.45),coth(1.45)-1.1164541],_ +[1.46,1.1140167,coth(1.46),coth(1.46)-1.1140167],_ +[1.47,1.1116330,coth(1.47),coth(1.47)-1.1116330],_ +[1.48,1.1093017,coth(1.48),coth(1.48)-1.1093017],_ +[1.49,1.1070216,coth(1.49),coth(1.49)-1.1070216],_ +[1.50,1.1047914,coth(1.50),coth(1.50)-1.1047914],_ +[1.51,1.1026099,coth(1.51),coth(1.51)-1.1026099],_ +[1.52,1.1004760,coth(1.52),coth(1.52)-1.1004760],_ +[1.53,1.0983886,coth(1.53),coth(1.53)-1.0983886],_ +[1.54,1.0963465,coth(1.54),coth(1.54)-1.0963465],_ +[1.55,1.0943487,coth(1.55),coth(1.55)-1.0943487],_ +[1.56,1.0923942,coth(1.56),coth(1.56)-1.0923942],_ +[1.57,1.0904819,coth(1.57),coth(1.57)-1.0904819],_ +[1.58,1.0886109,coth(1.58),coth(1.58)-1.0886109],_ +[1.59,1.0867801,coth(1.59),coth(1.59)-1.0867801],_ +[1.60,1.0849887,coth(1.60),coth(1.60)-1.0849887],_ +[1.61,1.0832358,coth(1.61),coth(1.61)-1.0832358],_ +[1.62,1.0815204,coth(1.62),coth(1.62)-1.0815204],_ +[1.63,1.0798418,coth(1.63),coth(1.63)-1.0798418],_ +[1.64,1.0781990,coth(1.64),coth(1.64)-1.0781990],_ +[1.65,1.0765913,coth(1.65),coth(1.65)-1.0765913],_ +[1.66,1.0750178,coth(1.66),coth(1.66)-1.0750178],_ +[1.67,1.0734777,coth(1.67),coth(1.67)-1.0734777],_ +[1.68,1.0719704,coth(1.68),coth(1.68)-1.0719704],_ +[1.69,1.0704951,coth(1.69),coth(1.69)-1.0704951],_ +[1.70,1.0690510,coth(1.70),coth(1.70)-1.0690510],_ +[1.71,1.0676375,coth(1.71),coth(1.71)-1.0676375],_ +[1.72,1.0662538,coth(1.72),coth(1.72)-1.0662538],_ +[1.73,1.0648993,coth(1.73),coth(1.73)-1.0648993],_ +[1.74,1.0635734,coth(1.74),coth(1.74)-1.0635734],_ +[1.75,1.0622753,coth(1.75),coth(1.75)-1.0622753],_ +[1.76,1.0610046,coth(1.76),coth(1.76)-1.0610046],_ +[1.77,1.0597605,coth(1.77),coth(1.77)-1.0597605],_ +[1.78,1.0585425,coth(1.78),coth(1.78)-1.0585425],_ +[1.79,1.0573501,coth(1.79),coth(1.79)-1.0573501],_ +[1.80,1.0561826,coth(1.80),coth(1.80)-1.0561826],_ +[1.81,1.0550395,coth(1.81),coth(1.81)-1.0550395],_ +[1.82,1.0539202,coth(1.82),coth(1.82)-1.0539202],_ +[1.83,1.0528243,coth(1.83),coth(1.83)-1.0528243],_ +[1.84,1.0517513,coth(1.84),coth(1.84)-1.0517513],_ +[1.85,1.0507005,coth(1.85),coth(1.85)-1.0507005],_ +[1.86,1.0496717,coth(1.86),coth(1.86)-1.0496717],_ +[1.87,1.0486642,coth(1.87),coth(1.87)-1.0486642],_ +[1.88,1.0476776,coth(1.88),coth(1.88)-1.0476776],_ +[1.89,1.0467115,coth(1.89),coth(1.89)-1.0467115],_ +[1.90,1.0457653,coth(1.90),coth(1.90)-1.0457653],_ +[1.91,1.0448388,coth(1.91),coth(1.91)-1.0448388],_ +[1.92,1.0439314,coth(1.92),coth(1.92)-1.0439314],_ +[1.93,1.0430428,coth(1.93),coth(1.93)-1.0430428],_ +[1.94,1.0421725,coth(1.94),coth(1.94)-1.0421725],_ +[1.95,1.0413202,coth(1.95),coth(1.95)-1.0413202],_ +[1.96,1.0404855,coth(1.96),coth(1.96)-1.0404855],_ +[1.97,1.0396679,coth(1.97),coth(1.97)-1.0396679],_ +[1.98,1.0388672,coth(1.98),coth(1.98)-1.0388672],_ +[1.99,1.0380829,coth(1.99),coth(1.99)-1.0380829],_ +[2.00,1.0373147,coth(2.00),coth(2.00)-1.0373147]] +--R +--R +--R (2) +--R [[0.01,100.0033333,100.0033333111 1132275,0.3111113227 5 E -6], +--R [0.02,50.0066665,50.0066664888 95661105,- 0.111043389 E -7], +--R [0.03,33.3433327,33.3433327333 84757277,0.3338475727 7 E -7], +--R [0.04,25.0133319,25.0133319113 27796018,0.1132779602 E -7], +--R [0.05,20.0166639,20.0166638895 50099248,- 0.1044990075 E -7], +--R 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New York 1965. pp213-216 +\end{thebibliography} +\end{document}