The value of Zeta(3) to 1,000,000 Places potx

Project Gutenberg Etext The value ofZeta3 to 1,000,000 Places #19 in ourseries of math constantsCopyright laws are changing all over theworld, be sure to check the copyright lawsfor your

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Title: The value of Zeta(3) to 1,000,000decimal digits the number is defined assum(1/n^3,n=1 infinity), the sum ofinverses of cubes and equals

1.2020569031…

Editor: Simon Plouffe

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Mathematical constants and numbersedited by Simon Plouffe Associate

Professor LaCIM, University of Quebec atMontreal http://www.lacim.uqam.ca/pi :Plouffe's Inverter plouffe@math.uqam.ca

The value of Zeta(3) to 1,000,000 decimaldigits the number is defined as

sum(1/n^3,n=1 infinity), the sum of

inverses of cubes and equals

1.2020569031…

Computed by : Sebastian Wedeniwski(wedeniws@de.ibm.com) who computedmore than 128 million digits using this

more efficient formula found by TheodorAmdeberhan and Doron Zeilberger.

| ——— (3 n + 2)! ((4 n +3)!) |

\ n >= 0 /

5 4 3 2 with A(n) := 126392 n + 412708 n+ 531578 n + 336367 n + 104000 n +

12463 given by Theodor Amdeberhan and

Doron Zeilberger (see [1]).

References: ===========

[1] T Amdeberhan und D Zeilberger:Hypergeometric Series Acceleration via the WZ Method, Electronic Journal ofCombinatorics (Wilf Festschrift

Volume) 4 (1997)

[2] B Haible, T Papanikolaou: Fastmultiprecision evaluation of series of rational numbers, Technical Report TI-97-7, Darmstadt University of

University, available by anonymous ftpfrom "ftp://ftp.informatik.uni-

tuebingen.de/pub/CA/software/Piologie/"

or

"ftp://ruediger.informatik.uni-tuebingen.de/Piologie/"

End of Project Gutenberg Etext The value

of Zeta(3) to 1,000,000 Places