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/axiomwebsite/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 9196. (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/199766218/S0025571897008569/S0025571897008569.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/axiomwebsite/patches.html 20150411.01.tpd.patch
+20150411 tpd books/bookvolbib add Bail97
20150410 tpd src/axiomwebsite/patches.html 20150410.01.tpd.patch
20150410 tpd readme add Kevlin Henney quote
20150408 tpd src/axiomwebsite/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/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 5705359..9929c67 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5008,6 +5008,8 @@ books/bookvol5 inline msgs, add trace chapter head
src/doc/msgs/coeng.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