// PiFast, copyright 1999-2001 Xavier Gourdon 
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       *    User constant file definition    *
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Version : 4.0
Constant name : Zeta3_Zeilberger2
Comments :

Formula from T. Amdeberhan and D. Zeilberger :

              ----                                   
              \          n    P(n)*((2n+1)! (2n)! n!)^3
   Zeta(3)  = /      (-1)   ---------------------------- 
              ----            24  (3n+2)! ((4n+3)!)^3
              0<=n<N

where P(n) = 126392 n^5 + 412708 n^4 + 531578 n^3 + 336367 n^2 + 104000 n + 12463.

This formula was used to break the record computation of zeta(3) 
at 128 million digits in Dec. 1998 by S. Wedeniwski.
.
Number of series : 1

Series number 0
Beta : 1
Series type : 0
Definition mode : 1
Alpha : 12463/10368
Beta : 12463/10368
Polynomial F : (126392*n^5+412708*n^4+531578*n^3+336367*n^2+104000*n+12463)*n^5*(2n-1)^3
Polynomial G : (126392*(n-1)^5+412708*(n-1)^4+531578*(n-1)^3+336367*(n-1)^2+104000*(n-1)+12463)*24*(3n+1)*(3n+2)*(4n+1)^3*(4n+3)^3
Z : -1

Approximate value : zeta3 = 1.202056903160