diff --git a/changelog b/changelog index c83bc01..37c11ce 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100620 tpd src/axiom-website/patches.html 20100620.03.tpd.patch +20100620 tpd src/input/Makefile integral function integration +20100620 tpd src/input/richintfunc000-032.input integral function integration 20100620 tpd src/axiom-website/patches.html 20100620.02.tpd.patch 20100620 tpd src/input/Makefile error function integration 20100620 tpd src/input/richerror000-078.input error function integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 534a6f2..fe405de 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2930,6 +2930,8 @@ src/input/richinvhyper100-199.input inverse hyperbolic int.
src/input/richinvhyper200-296.input inverse hyperbolic int.
20100620.02.tpd.patch src/input/richerror000-078.input error function integration
+20100620.03.tpd.patch +src/input/richintfunc000-032.input integral function integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index d019c1c..59ef11e 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -387,6 +387,7 @@ REGRES= ackermann.regress \ richhyper800-899.regress \ richhyper900-999.regress \ richhyper1000-1098.regress \ + richintfunc000-032.regress \ richinvhyper000-099.regress \ richinvhyper100-199.regress \ richinvhyper200-296.regress \ @@ -736,6 +737,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper800-899.input \ ${OUT}/richhyper900-999.input \ ${OUT}/richhyper1000-1098.input \ + ${OUT}/richintfunc000-032.input \ ${OUT}/richinvhyper000-099.input \ ${OUT}/richinvhyper100-199.input \ ${OUT}/richinvhyper200-296.input \ @@ -1114,6 +1116,7 @@ DOCFILES= \ ${DOC}/richhyper800-899.input.dvi \ ${DOC}/richhyper900-999.input.dvi \ ${DOC}/richhyper1000-1098.input.dvi \ + ${DOC}/richintfunc000-032.input.dvi \ ${DOC}/richinvhyper000-099.input.dvi \ ${DOC}/richinvhyper100-199.input.dvi \ ${DOC}/richinvhyper200-296.input.dvi \ diff --git a/src/input/richintfunc000-032.input.pamphlet b/src/input/richintfunc000-032.input.pamphlet new file mode 100644 index 0000000..a52f4fb --- /dev/null +++ b/src/input/richintfunc000-032.input.pamphlet @@ -0,0 +1,1787 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richintfunc000-032.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richintfunc000-032.output +)spool richintfunc000-032.output +)set message auto off +)clear all + +--S 1 of 165 +t0000:= x^m*Ei(b*x) +--R +--R +--R m +--R (1) Ei(b x)x +--R Type: Expression Integer +--E 1 + +--S 2 of 165 +r0000:= -1/b/(1+m)*(-x^(1+m)*Ei(b*x)*b+x^m*(-b*x)^(-m)*Gamma(1+m,-b*x)) +--R +--R +--R - m m _ m + 1 +--R - (- b x) x | (m + 1,- b x) + b Ei(b x)x +--R (2) ----------------------------------------------- +--R b m + b +--R Type: Expression Integer +--E 2 + +--S 3 of 165 +--a0000:= integrate(t0000,x) +--E 3 + +--S 4 of 165 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 165 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 165 +t0001:= exp(1)^(b*x)*Ei(b*x)/x^3 +--R +--R +--R b x +--R Ei(b x)%e +--R (3) ------------ +--R 3 +--R x +--R Type: Expression Integer +--E 6 + +--S 7 of 165 +r0001:= -1/4*(exp(2*b*x)+4*exp(2*b*x)*b*x+2*Ei(b*x)*exp(b*x)+_ + 2*Ei(b*x)*exp(b*x)*b*x-x^2*Ei(b*x)^2*b^2-8*b^2*Ei(2*b*x)*x^2)/x^2 +--R +--R +--R (4) +--R 2b x b x 2 2 2 2 2 +--R (- 4b x - 1)%e + (- 2b x - 2)Ei(b x)%e + 8b x Ei(2b x) + b x Ei(b x) +--R ---------------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 7 + +--S 8 of 165 +--a0001:= integrate(t0001,x) +--E 8 + +--S 9 of 165 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 165 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 165 +t0002:= exp(1)^(b*x)*Ei(b*x)/x^2 +--R +--R +--R b x +--R Ei(b x)%e +--R (5) ------------ +--R 2 +--R x +--R Type: Expression Integer +--E 11 + +--S 12 of 165 +r0002:= -1/2*(2*exp(2*b*x)+2*Ei(b*x)*exp(b*x)-x*Ei(b*x)^2*b-4*b*Ei(2*b*x)*x)/x +--R +--R +--R 2b x b x 2 +--R - 2%e - 2Ei(b x)%e + 4b x Ei(2b x) + b x Ei(b x) +--R (6) -------------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 12 + +--S 13 of 165 +--a0002:= integrate(t0002,x) +--E 13 + +--S 14 of 165 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 165 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 165 +t0003:= x*exp(1)^(a+b*x)*Ei(c+d*x) +--R +--R +--R b x + a +--R (7) x Ei(d x + c)%e +--R Type: Expression Integer +--E 16 + +--S 17 of 165 +r0003:= -exp(1)^(a+c+(b+d)*x)/b/(b+d)-exp(1)^(a+b*x)*(1-b*x)*Ei(c+d*x)/b^2+_ + (b*c+d)*exp(1)^(a-b*c/d)*Ei((b+d)*(c+d*x)/d)/b^2/d +--R +--R +--R (8) +--R (d + b)x + c + a 2 2 2 b x + a +--R - b d %e + ((b d + b d)x - d - b d)Ei(d x + c)%e +--R + +--R a d - b c +--R 2 --------- +--R 2 2 (d + b d)x + c d + b c d +--R (d + (b c + b)d + b c)Ei(-----------------------)%e +--R d +--R / +--R 2 2 3 +--R b d + b d +--R Type: Expression Integer +--E 17 + +--S 18 of 165 +--a0003:= integrate(t0003,x) +--E 18 + +--S 19 of 165 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 165 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 165 +t0004:= x^2*exp(1)^(a+b*x)*Ei(c+d*x) +--R +--R +--R 2 b x + a +--R (9) x Ei(d x + c)%e +--R Type: Expression Integer +--E 21 + +--S 22 of 165 +r0004:= exp(1)^(a+c+(b+d)*x)/b/(b+d)^2+2*exp(1)^(a+c+(b+d)*x)/b^2/(b+d)+_ + c*exp(1)^(a+c+(b+d)*x)/b/d/(b+d)-exp(1)^(a+c+(b+d)*x)*_ + x/b/(b+d)+exp(1)^(a+b*x)*(2-2*b*x+b^2*x^2)*Ei(c+d*x)/b^3-_ + (b^2*c^2+2*b*c*d+2*d^2)*exp(1)^(a-b*c/d)*Ei((b+d)*(c+d*x)/d)/b^3/d^2 +--R +--R +--R (10) +--R 2 3 3 2 3 2 2 2 3 (d + b)x + c + a +--R ((- b d - b d )x + 2b d + (b c + 3b )d + b c d)%e +--R + +--R 2 4 3 3 4 2 2 4 2 3 3 2 4 3 +--R (b d + 2b d + b d )x + (- 2b d - 4b d - 2b d )x + 2d + 4b d +--R + +--R 2 2 +--R 2b d +--R * +--R b x + a +--R Ei(d x + c)%e +--R + +--R 4 3 2 2 2 2 2 3 2 3 +--R - 2d + (- 2b c - 4b)d + (- b c - 4b c - 2b )d + (- 2b c - 2b c)d +--R + +--R 4 2 +--R - b c +--R * +--R a d - b c +--R 2 --------- +--R (d + b d)x + c d + b c d +--R Ei(-----------------------)%e +--R d +--R / +--R 3 4 4 3 5 2 +--R b d + 2b d + b d +--R Type: Expression Integer +--E 22 + +--S 23 of 165 +--a0004:= integrate(t0004,x) +--E 23 + +--S 24 of 165 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 165 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 165 +t0005:= x^m*Si(b*x) +--R +--R +--R m +--R (11) Si(b x)x +--R Type: Expression Integer +--E 26 + +--S 27 of 165 +r0005:= 1/2*(x^m*(-%i*b*x)^(-m)*Gamma(1+m,-%i*b*x)+x^m*(%i*b*x)^(-m)*_ + Gamma(1+m,%i*b*x)+2*x^(1+m)*Si(b*x)*b)/b/(1+m) +--R +--R +--R (12) +--R m - m _ - m m _ +--R x (%i b x) | (m + 1,%i b x) + (- %i b x) x | (m + 1,- %i b x) +--R + +--R m + 1 +--R 2b Si(b x)x +--R / +--R 2b m + 2b +--R Type: Expression Complex Integer +--E 27 + +--S 28 of 165 +--a0005:= integrate(t0005,x) +--E 28 + +--S 29 of 165 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 165 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 165 +t0006:= sin(b*x)*Si(b*x)/x^3 +--R +--R +--R Si(b x)sin(b x) +--R (13) --------------- +--R 3 +--R x +--R Type: Expression Integer +--E 31 + +--S 32 of 165 +r0006:= -1/4*(-4*b^2*Ci(2*b*x)*x^2+2*x*cos(b*x)*sin(b*x)*b+1-_ + cos(b*x)^2+x*b*sin(2*b*x)+2*x*cos(b*x)*Si(b*x)*b+2*sin(b*x)*Si(b*x)+_ + x^2*Si(b*x)^2*b^2)/x^2 +--R +--R +--R (14) +--R 2 +--R - b x sin(2b x) + (- 2b x cos(b x) - 2Si(b x))sin(b x) + cos(b x) +--R + +--R 2 2 2 2 2 +--R - 2b x Si(b x)cos(b x) - b x Si(b x) + 4b x Ci(2b x) - 1 +--R / +--R 2 +--R 4x +--R Type: Expression Integer +--E 32 + +--S 33 of 165 +a0006:= integrate(t0006,x) +--R +--R +--R x +--R ++ Si(%A b)sin(%A b) +--R (15) | ----------------- d%A +--R ++ 3 +--R %A +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 165 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 165 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 165 +t0007:= x*sin(a+b*x)*Si(c+d*x) +--R +--R +--R (16) x Si(d x + c)sin(b x + a) +--R Type: Expression Integer +--E 36 + +--S 37 of 165 +r0007:= 1/2*cos(a-c+(b-d)*x)/b/(b-d)-1/2*cos(a+c+(b+d)*x)/b/(b+d)-_ + 1/2*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b^2+_ + 1/2*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*Ci((b-d)*(c+d*x)/d)*sin(a-b*c/d)/b/d-_ + 1/2*c*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b/d-x*cos(a+b*x)*Si(c+d*x)/b+_ + sin(a+b*x)*Si(c+d*x)/b^2+1/2*c*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b/d+_ + 1/2*sin(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2-_ + 1/2*c*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d-_ + 1/2*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2 +--R +--R +--R (17) +--R 3 2 +--R (2d - 2b d)Si(d x + c)sin(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (b c d - b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 2 2 2 2 +--R (- b d + b d)cos((d + b)x + c + a) + (- b d - b d)cos((d - b)x + c - a) +--R + +--R 3 3 +--R (- 2b d + 2b d)x Si(d x + c)cos(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (d - b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (- d + b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression Integer +--E 37 + +--S 38 of 165 +a0007:= integrate(t0007,x) +--R +--R +--R x +--R ++ +--R (18) | %A Si(%A d + c)sin(%A b + a)d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 165 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 165 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 165 +t0008:= cos(b*x)*Si(b*x)/x^2 +--R +--R +--R Si(b x)cos(b x) +--R (19) --------------- +--R 2 +--R x +--R Type: Expression Integer +--E 41 + +--S 42 of 165 +r0008:= -1/2*(-2*b*Ci(2*b*x)*x+sin(2*b*x)+2*cos(b*x)*Si(b*x)+x*Si(b*x)^2*b)/x +--R +--R +--R 2 +--R - sin(2b x) - 2Si(b x)cos(b x) - b x Si(b x) + 2b x Ci(2b x) +--R (20) ------------------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 42 + +--S 43 of 165 +a0008:= integrate(t0008,x) +--R +--R +--R x +--R ++ Si(%A b)cos(%A b) +--R (21) | ----------------- d%A +--R ++ 2 +--R %A +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 165 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 165 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 165 +t0009:= x*cos(a+b*x)*Si(c+d*x) +--R +--R +--R (22) x Si(d x + c)cos(b x + a) +--R Type: Expression Integer +--E 46 + +--S 47 of 165 +r0009:= 1/2*c*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b/d-_ + 1/2*c*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b/d+_ + 1/2*Ci((b-d)*(c+d*x)/d)*sin(a-b*c/d)/b^2-_ + 1/2*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b^2-_ + 1/2*sin(a-c+(b-d)*x)/b/(b-d)+1/2*sin(a+c+(b+d)*x)/b/_ + (b+d)+cos(a+b*x)*Si(c+d*x)/b^2+x*sin(a+b*x)*Si(c+d*x)/b+_ + 1/2*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2-_ + 1/2*c*sin(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b/d-_ + 1/2*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d +--R +--R +--R (23) +--R 2 2 2 2 +--R (b d - b d)sin((d + b)x + c + a) + (- b d - b d)sin((d - b)x + c - a) +--R + +--R 3 3 +--R (2b d - 2b d)x Si(d x + c)sin(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (d - b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 3 2 +--R (2d - 2b d)Si(d x + c)cos(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (b c d - b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression Integer +--E 47 + +--S 48 of 165 +a0009:= integrate(t0009,x) +--R +--R +--R x +--R ++ +--R (24) | %A Si(%A d + c)cos(%A b + a)d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 165 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 165 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 165 +t0010:= x^m*Ci(b*x) +--R +--R +--R m +--R (25) Ci(b x)x +--R Type: Expression Integer +--E 51 + +--S 52 of 165 +r0010:= 1/2*(%i*x^m*(-%i*b*x)^(-m)*Gamma(1+m,-%i*b*x)-%i*x^m*(%i*b*x)^(-m)*_ + Gamma(1+m,%i*b*x)+2*x^(1+m)*Ci(b*x)*b)/b/(1+m) +--R +--R +--R (26) +--R m - m _ - m m _ +--R - %i x (%i b x) | (m + 1,%i b x) + %i (- %i b x) x | (m + 1,- %i b x) +--R + +--R m + 1 +--R 2b Ci(b x)x +--R / +--R 2b m + 2b +--R Type: Expression Complex Integer +--E 52 + +--S 53 of 165 +a0010:= integrate(t0010,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 53 + +--S 54 of 165 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 165 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 165 +t0011:= Ci(b*x)*sin(b*x)/x^2 +--R +--R +--R Ci(b x)sin(b x) +--R (27) --------------- +--R 2 +--R x +--R Type: Expression Integer +--E 56 + +--S 57 of 165 +r0011:= -1/2*(-x*Ci(b*x)^2*b-2*b*Ci(2*b*x)*x+2*sin(b*x)*Ci(b*x)+sin(2*b*x))/x +--R +--R +--R 2 +--R - sin(2b x) - 2Ci(b x)sin(b x) + 2b x Ci(2b x) + b x Ci(b x) +--R (28) ------------------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 57 + +--S 58 of 165 +a0011:= integrate(t0011,x) +--R +--R +--R x +--R ++ Ci(%A b)sin(%A b) +--R (29) | ----------------- d%A +--R ++ 2 +--R %A +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 165 +--m0011:= a0011-r0011 +--E 59 + +--S 60 of 165 +--d0011:= D(m0011,x) +--E 60 + +--S 61 of 165 +t0012:= x*sin(a+b*x)*Ci(c+d*x) +--R +--R +--R (30) x Ci(d x + c)sin(b x + a) +--R Type: Expression Integer +--E 61 + +--S 62 of 165 +r0012:= -x*cos(a+b*x)*Ci(c+d*x)/b-1/2*c*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b/d-_ + 1/2*c*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b/d-1/2*Ci((b-d)*(c+d*x)/d)*_ + sin(a-b*c/d)/b^2-1/2*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b^2+Ci(c+d*x)*_ + sin(a+b*x)/b^2+1/2*sin(a-c+(b-d)*x)/b/(b-d)+1/2*sin(a+c+(b+d)*x)/_ + b/(b+d)-1/2*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2+1/2*c*sin(a-b*c/d)*_ + Si((b-d)*(c+d*x)/d)/b/d-1/2*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d +--R +--R +--R (31) +--R 2 2 2 2 +--R (b d - b d)sin((d + b)x + c + a) + (b d + b d)sin((d - b)x + c - a) +--R + +--R 3 2 +--R (2d - 2b d)Ci(d x + c)sin(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (- d + b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 3 3 +--R (- 2b d + 2b d)x Ci(d x + c)cos(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (d - b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (- b c d + b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression Integer +--E 62 + +--S 63 of 165 +a0012:= integrate(t0012,x) +--R +--R +--R x +--R ++ +--R (32) | %A Ci(%A d + c)sin(%A b + a)d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 165 +--m0012:= a0012-r0012 +--E 64 + +--S 65 of 165 +--d0012:= D(m0012,x) +--E 65 + +--S 66 of 165 +t0013:= cos(b*x)*Ci(b*x)/x^3 +--R +--R +--R Ci(b x)cos(b x) +--R (33) --------------- +--R 3 +--R x +--R Type: Expression Integer +--E 66 + +--S 67 of 165 +r0013:= 1/4*(-cos(b*x)^2-2*cos(b*x)*Ci(b*x)-x^2*Ci(b*x)^2*b^2-_ + 4*b^2*Ci(2*b*x)*x^2+2*x*cos(b*x)*sin(b*x)*b+_ + 2*x*Ci(b*x)*sin(b*x)*b+x*b*sin(2*b*x))/x^2 +--R +--R +--R (34) +--R 2 +--R b x sin(2b x) + (2b x cos(b x) + 2b x Ci(b x))sin(b x) - cos(b x) +--R + +--R 2 2 2 2 2 +--R - 2Ci(b x)cos(b x) - 4b x Ci(2b x) - b x Ci(b x) +--R / +--R 2 +--R 4x +--R Type: Expression Integer +--E 67 + +--S 68 of 165 +a0013:= integrate(t0013,x) +--R +--R +--R x +--R ++ Ci(%A b)cos(%A b) +--R (35) | ----------------- d%A +--R ++ 3 +--R %A +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 165 +--m0013:= a0013-r0013 +--E 69 + +--S 70 of 165 +--d0013:= D(m0013,x) +--E 70 + +--S 71 of 165 +t0014:= x*cos(a+b*x)*Ci(c+d*x) +--R +--R +--R (36) x Ci(d x + c)cos(b x + a) +--R Type: Expression Integer +--E 71 + +--S 72 of 165 +r0014:= 1/2*cos(a-c+(b-d)*x)/b/(b-d)+1/2*cos(a+c+(b+d)*x)/b/(b+d)+_ + cos(a+b*x)*Ci(c+d*x)/b^2-1/2*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b^2-_ + 1/2*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*Ci((b-d)*(c+d*x)/d)*sin(a-b*c/d)/b/d+_ + 1/2*c*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b/d+_ + x*Ci(c+d*x)*sin(a+b*x)/b+1/2*c*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b/d+_ + 1/2*sin(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2+_ + 1/2*c*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d+_ + 1/2*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2 +--R +--R +--R (37) +--R 3 3 +--R (2b d - 2b d)x Ci(d x + c)sin(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (d - b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (b c d - b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 2 2 2 2 +--R (b d - b d)cos((d + b)x + c + a) + (- b d - b d)cos((d - b)x + c - a) +--R + +--R 3 2 +--R (2d - 2b d)Ci(d x + c)cos(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (- d + b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression Integer +--E 72 + +--S 73 of 165 +a0014:= integrate(t0014,x) +--R +--R +--R x +--R ++ +--R (38) | %A Ci(%A d + c)cos(%A b + a)d%A +--R ++ +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 165 +--m0014:= a0014-r0014 +--E 74 + +--S 75 of 165 +--d0014:= D(m0014,x) +--E 75 + +--S 76 of 165 +t0015:= x^m*Shi(b*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 76 + +--S 77 of 165 +r0015:= -1/2/b/(1+m)*(x^m*(b*x)^(-m)*Gamma(1+m,b*x)+x^m*(-b*x)^(-m)*_ + Gamma(1+m,-b*x)-2*x^(1+m)*Shi(b*x)*b) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 165 +--a0015:= integrate(t0015,x) +--E 78 + +--S 79 of 165 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 165 +--d0015:= D(m0015,x) +--E 80 + +--S 81 of 165 +t0016:= Shi(a+b*x)/x^3 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 165 +r0016:= 1/2*(b^2*cosh(a)*Chi(b*x)*a*x^2-b^2*Chi(b*x)*sinh(a)*x^2-_ + b*sinh(a+b*x)*a*x-b^2*cosh(a)*Shi(b*x)*x^2+b^2*sinh(a)*_ + Shi(b*x)*a*x^2+b^2*Shi(a+b*x)*x^2-Shi(a+b*x)*a^2)/a^2/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 165 +--a0016:= integrate(t0016,x) +--E 83 + +--S 84 of 165 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 165 +--d0016:= D(m0016,x) +--E 85 + +--S 86 of 165 +t0017:= Shi(a+b*x)/x^2 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 86 + +--S 87 of 165 +r0017:= (b*Chi(b*x)*sinh(a)*x+b*cosh(a)*Shi(b*x)*x-Shi(a+b*x)*b*x-_ + Shi(a+b*x)*a)/a/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 165 +--a0017:= integrate(t0017,x) +--E 88 + +--S 89 of 165 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 165 +--d0017:= D(m0017,x) +--E 90 + +--S 91 of 165 +t0018:= sinh(b*x)*Shi(b*x)/x^3 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 91 + +--S 92 of 165 +r0018:= -1/4*(-4*b^2*Chi(2*b*x)*x^2+2*x*cosh(b*x)*sinh(b*x)*b+cosh(b*x)^2-_ + 1+x*b*sinh(2*b*x)+2*x*cosh(b*x)*Shi(b*x)*b+2*sinh(b*x)*Shi(b*x)-_ + x^2*Shi(b*x)^2*b^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 165 +--a0018:= integrate(t0018,x) +--E 93 + +--S 94 of 165 +--m0018:= a0018-r0018 +--E 94 + +--S 95 of 165 +--d0018:= D(m0018,x) +--E 95 + +--S 96 of 165 +t0019:= sinh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 96 + +--S 97 of 165 +r0019:= 1/2*(Chi((b-d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)-_ + Chi((b+d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)+2*cosh(a+b*x)*Shi(c+d*x)+_ + cosh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)-_ + cosh((-b*c+a*d)/d)*Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 165 +--a0019:= integrate(t0019,x) +--E 98 + +--S 99 of 165 +--m0019:= a0019-r0019 +--E 99 + +--S 100 of 165 +--d0019:= D(m0019,x) +--E 100 + +--S 101 of 165 +t0020:= x*sinh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 101 + +--S 102 of 165 +r0020:= 1/2*cosh(a-c+(b-d)*x)/b/(b-d)-1/2*cosh(a+c+(b+d)*x)/b/(b+d)-_ + 1/2*cosh(a-b*c/d)*Chi((b-d)*(c+d*x)/d)/b^2+_ + 1/2*cosh(a-b*c/d)*Chi((b+d)*(c+d*x)/d)/b^2-_ + 1/2*c*Chi((b-d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+_ + 1/2*c*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+x*cosh(a+b*x)*_ + Shi(c+d*x)/b-sinh(a+b*x)*Shi(c+d*x)/b^2-1/2*c*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d-1/2*sinh(a-b*c/d)*Shi((b-d)*(c+d*x)/d)/b^2+_ + 1/2*c*cosh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b/d+_ + 1/2*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 165 +--a0020:= integrate(t0020,x) +--E 103 + +--S 104 of 165 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 165 +--d0020:= D(m0020,x) +--E 105 + +--S 106 of 165 +t0021:= cosh(b*x)*Shi(b*x)/x^2 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 106 + +--S 107 of 165 +r0021:= 1/2*(2*b*Chi(2*b*x)*x-sinh(2*b*x)-_ + 2*cosh(b*x)*Shi(b*x)+x*Shi(b*x)^2*b)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 165 +--a0021:= integrate(t0021,x) +--E 108 + +--S 109 of 165 +--m0021:= a0021-r0021 +--E 109 + +--S 110 of 165 +--d0021:= D(m0021,x) +--E 110 + +--S 111 of 165 +t0022:= cosh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 111 + +--S 112 of 165 +r0022:= -1/2*(-cosh((-b*c+a*d)/d)*Chi((b-d)*(c+d*x)/d)+_ + cosh((-b*c+a*d)/d)*Chi((b+d)*(c+d*x)/d)-_ + 2*sinh(a+b*x)*Shi(c+d*x)-sinh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)+_ + sinh((-b*c+a*d)/d)*Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 165 +--a0022:= integrate(t0022,x) +--E 113 + +--S 114 of 165 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 165 +--d0022:= D(m0022,x) +--E 115 + +--S 116 of 165 +t0023:= x*cosh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 116 + +--S 117 of 165 +r0023:= -1/2*c*cosh(a-b*c/d)*Chi((b-d)*(c+d*x)/d)/b/d+_ + 1/2*c*cosh(a-b*c/d)*Chi((b+d)*(c+d*x)/d)/b/d-_ + 1/2*Chi((b-d)*(c+d*x)/d)*sinh(a-b*c/d)/b^2+_ + 1/2*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b^2+_ + 1/2*sinh(a-c+(b-d)*x)/b/(b-d)-_ + 1/2*sinh(a+c+(b+d)*x)/b/(b+d)-cosh(a+b*x)*Shi(c+d*x)/b^2+_ + x*sinh(a+b*x)*Shi(c+d*x)/b-1/2*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b^2-1/2*c*sinh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d+1/2*cosh(a-b*c/d)*_ + Shi((b+d)*(c+d*x)/d)/b^2+1/2*c*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b/d +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 165 +--a0023:= integrate(t0023,x) +--E 118 + +--S 119 of 165 +--m0023:= a0023-r0023 +--E 119 + +--S 120 of 165 +--d0023:= D(m0023,x) +--E 120 + +--S 121 of 165 +t0024:= x^m*Chi(b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 121 + +--S 122 of 165 +r0024:= 1/2/b/(1+m)*(x^m*(b*x)^(-m)*Gamma(1+m,b*x)-x^m*(-b*x)^(-m)*_ + Gamma(1+m,-b*x)+2*x^(1+m)*Chi(b*x)*b) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 165 +--a0024:= integrate(t0024,x) +--E 123 + +--S 124 of 165 +--m0024:= a0024-r0024 +--E 124 + +--S 125 of 165 +--d0024:= D(m0024,x) +--E 125 + +--S 126 of 165 +t0025:= Chi(a+b*x)/x^3 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 126 + +--S 127 of 165 +r0025:= -1/2*(b*cosh(a+b*x)*a*x+b^2*cosh(a)*Chi(b*x)*x^2-_ + b^2*Chi(a+b*x)*x^2+Chi(a+b*x)*a^2-b^2*Chi(b*x)*sinh(a)*a*x^2-_ + b^2*cosh(a)*Shi(b*x)*a*x^2+b^2*sinh(a)*Shi(b*x)*x^2)/a^2/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 165 +--a0025:= integrate(t0025,x) +--E 128 + +--S 129 of 165 +--m0025:= a0025-r0025 +--E 129 + +--S 130 of 165 +--d0025:= D(m0025,x) +--E 130 + +--S 131 of 165 +t0026:= Chi(a+b*x)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 131 + +--S 132 of 165 +r0026:= (b*cosh(a)*Chi(b*x)*x-Chi(a+b*x)*b*x-Chi(a+b*x)*a+_ + b*sinh(a)*Shi(b*x)*x)/a/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 165 +--a0026:= integrate(t0026,x) +--E 133 + +--S 134 of 165 +--m0026:= a0026-r0026 +--E 134 + +--S 135 of 165 +--d0026:= D(m0026,x) +--E 135 + +--S 136 of 165 +t0027:= Chi(b*x)*sinh(b*x)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 136 + +--S 137 of 165 +r0027:= 1/2*(x*Chi(b*x)^2*b+2*b*Chi(2*b*x)*x-2*sinh(b*x)*Chi(b*x)-_ + sinh(2*b*x))/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 165 +--a0027:= integrate(t0027,x) +--E 138 + +--S 139 of 165 +--m0027:= a0027-r0027 +--E 139 + +--S 140 of 165 +--d0027:= D(m0027,x) +--E 140 + +--S 141 of 165 +t0028:= sinh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 141 + +--S 142 of 165 +r0028:= -1/2*(-2*cosh(a+b*x)*Chi(c+d*x)+cosh((-b*c+a*d)/d)*_ + Chi((b-d)*(c+d*x)/d)+cosh((-b*c+a*d)/d)*Chi((b+d)*(c+d*x)/d)+_ + sinh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)+sinh((-b*c+a*d)/d)*_ + Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 165 +--a0028:= integrate(t0028,x) +--E 143 + +--S 144 of 165 +--m0028:= a0028-r0028 +--E 144 + +--S 145 of 165 +--d0028:= D(m0028,x) +--E 145 + +--S 146 of 165 +t0029:= x*sinh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 146 + +--S 147 of 165 +r0029:= x*cosh(a+b*x)*Chi(c+d*x)/b+1/2*c*cosh(a-b*c/d)*_ + Chi((b-d)*(c+d*x)/d)/b/d+1/2*c*cosh(a-b*c/d)*_ + Chi((b+d)*(c+d*x)/d)/b/d+1/2*Chi((b-d)*(c+d*x)/d)*_ + sinh(a-b*c/d)/b^2+1/2*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b^2-_ + Chi(c+d*x)*sinh(a+b*x)/b^2-1/2*sinh(a-c+(b-d)*x)/b/(b-d)-_ + 1/2*sinh(a+c+(b+d)*x)/b/(b+d)+1/2*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b^2+1/2*c*sinh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d+1/2*cosh(a-b*c/d)*_ + Shi((b+d)*(c+d*x)/d)/b^2+1/2*c*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b/d +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 165 +--a0029:= integrate(t0029,x) +--E 148 + +--S 149 of 165 +--m0029:= a0029-r0029 +--E 149 + +--S 150 of 165 +--d0029:= D(m0029,x) +--E 150 + +--S 151 of 165 +t0030:= cosh(b*x)*Chi(b*x)/x^3 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 151 + +--S 152 of 165 +r0030:= 1/4*(-cosh(b*x)^2-2*cosh(b*x)*Chi(b*x)+x^2*Chi(b*x)^2*b^2+_ + 4*b^2*Chi(2*b*x)*x^2-2*x*cosh(b*x)*sinh(b*x)*b-_ + 2*x*Chi(b*x)*sinh(b*x)*b-x*b*sinh(2*b*x))/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 165 +--a0030:= integrate(t0030,x) +--E 153 + +--S 154 of 165 +--m0030:= a0030-r0030 +--E 154 + +--S 155 of 165 +--d0030:= D(m0030,x) +--E 155 + +--S 156 of 165 +t0031:= cosh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 165 +r0031:= -1/2*(Chi((b-d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)+_ + Chi((b+d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)-2*sinh(a+b*x)*_ + Chi(c+d*x)+cosh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)+_ + cosh((-b*c+a*d)/d)*Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 165 +--a0031:= integrate(t0031,x) +--E 158 + +--S 159 of 165 +--m0031:= a0031-r0031 +--E 159 + +--S 160 of 165 +--d0031:= D(m0031,x) +--E 160 + +--S 161 of 165 +t0032:= x*cosh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 161 + +--S 162 of 165 +r0032:= -1/2*cosh(a-c+(b-d)*x)/b/(b-d)-1/2*cosh(a+c+(b+d)*x)/b/(b+d)-_ + cosh(a+b*x)*Chi(c+d*x)/b^2+1/2*cosh(a-b*c/d)*_ + Chi((b-d)*(c+d*x)/d)/b^2+1/2*cosh(a-b*c/d)*Chi((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*Chi((b-d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+_ + 1/2*c*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+x*_ + Chi(c+d*x)*sinh(a+b*x)/b+1/2*c*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d+1/2*sinh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b^2+1/2*c*cosh(a-b*c/d)*_ + Shi((b+d)*(c+d*x)/d)/b/d+1/2*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 165 +--a0032:= integrate(t0032,x) +--E 163 + +--S 164 of 165 +--m0032:= a0032-r0032 +--E 164 + +--S 165 of 165 +--d0032:= D(m0032,x) +--E 165 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}