From 67fd9ced865b0e375376c4cf9e404e29735ee7c5 Mon Sep 17 00:00:00 2001 From: Tim Daly Date: Sat, 11 Apr 2015 16:31:36 -0400 Subject: [PATCH] books/bookvolbib add Bail97 author = "Bailey, David and Borwein, Peter and Plouffe, Simon", title = "On the Rapid Computation of Various Polylogarithmic Constants", --- books/bookvolbib.pamphlet | 37 +++++++++++++++++++++++++++++++++++++ changelog | 2 ++ patch | 10 +++------- src/axiom-website/patches.html | 2 ++ 4 files changed, 44 insertions(+), 7 deletions(-) diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet index c418677..896157e 100644 --- a/books/bookvolbib.pamphlet +++ b/books/bookvolbib.pamphlet @@ -15974,6 +15974,43 @@ Math. Tables Aids Comput. 10 91--96. (1956) \end{chunk} +\index{Bailey, David} +\index{Borwein, Peter} +\index{Plouffe, Simon} +\begin{chunk}{axiom.bib} +@misc{Bail97 + author = "Bailey, David and Borwein, Peter and Plouffe, Simon", + title = "On the Rapid Computation of Various Polylogarithmic Constants", + year = "1997", + url = "http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf", + paper = "Bail97.pdf", + abstract = " + We give algorithms for the computation of the $d$-th digit of certain + transcendental numbers in various bases. These algorithms can be + easily implemented (multiple precision arithmetic is not needed), + require virtually no memeory, and feature run times that scale nearly + linearly with the order of the digit desired. They make it feasible to + compute, for example, the billionth binary digit of log(2) or $\pi$ on + a modest work station in a few hours run time. + + We demonstrate this technique by computing the ten billionth + hexadecimal digit of $\pi$, the billionth hexadecimal digits of + $\pi^2$, log(2), and log${}^2$(2), and the ten billionth decimal digit + of log(9/10). + + These calculations rest on the observation that very special types of + identities exist for certain numbers like $\pi$, $\pi^2$, log(2) and + log${}^2$. These are essentially polylogarithmic ladders in an integer + base. A number of these identities that we derive in this work appear + to be new, for example the critical identity for $\pi$: + + \[\pi=\sum_{i=0}^\infty{\frac{1}{16^i}\left( + \frac{4}{8i+1}-\frac{2}{8i+4}-\frac{1}{8i+5}-\frac{1}{8i+6}\right)\]" + +} + +\end{chunk} + \eject %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Bibliography} diff --git a/changelog b/changelog index 64cb615..13e6bfd 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20150411 tpd src/axiom-website/patches.html 20150411.01.tpd.patch +20150411 tpd books/bookvolbib add Bail97 20150410 tpd src/axiom-website/patches.html 20150410.01.tpd.patch 20150410 tpd readme add Kevlin Henney quote 20150408 tpd src/axiom-website/patches.html 20150408.01.tpd.patch diff --git a/patch b/patch index 4215460..9544533 100644 --- a/patch +++ b/patch @@ -1,8 +1,4 @@ -readme add Kevlin Henney quote +books/bookvolbib add Bail97 - "A common fallacy is to assume authors of incomprehensilbe code - will somehow be able to express themselves lucidly and clearly - in comments." -- Kevlin Henney - - "A programmer who cannot explain their ideas clearly in natural - language is incapable of writing readable code." -- Tim Daly +author = "Bailey, David and Borwein, Peter and Plouffe, Simon", +title = "On the Rapid Computation of Various Polylogarithmic Constants", diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 5705359..9929c67 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -5008,6 +5008,8 @@ books/bookvol5 inline msgs, add trace chapter head
src/doc/msgs/co-eng.msgs remove unused file
20150410.01.tpd.patch readme add Kevlin Henney quote
+20150411.01.tpd.patch +books/bookvolbib add Bail97
-- 1.7.5.4