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The Value of Zeta(3) to 1,000,000 places   By: (1956-)

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Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.ca

The value of Zeta(3) to 1,000,000 decimal digits. 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 computed more than 128 million digits using this more efficient formula found by Theodor Amdeberhan and Doron Zeilberger.

/ \ 3 \ n A(n) ((2 n 1)! (2 n)! n!) Zeta(3) = 1/24 ) ( 1) / 3 (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 of Combinatorics (Wilf Festschrift Volume) 4 (1997).

[2] B. Haible, T. Papanikolaou: Fast multiprecision evaluation of series of rational numbers, Technical Report TI 97 7, Darmstadt University of Technology, April 1997.

[3] S. Wedeniwski: Piologie Eine exakte arithmetische Bibliothek in C, Technical Report WSI 96 35, Tuebingen University, available by anonymous ftp from "ftp://ftp.informatik.uni tuebingen.de/pub/CA/software/Piologie/" or "ftp://ruediger.informatik.uni tuebingen.de/Piologie/".

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