// PiFast, copyright 1999-2001 Xavier Gourdon *************************************** * * * User constant file definition * * * *************************************** Version : 4.0 Constant name : Zeta3_Apery Comments : zeta(3) is defined by zeta(3) = sum_{n>0} 1/n^3 Formula used : zeta(3) = 5/2 * sum_{n>0} (-1)^n * (n!)^2/n^3/(2n)! (Apery 1978) . Number of series : 1 Series number 0 Beta : 5/2 Series type : 0 Definition mode : 1 Alpha : 1/2 Beta : 1/2 Polynomial F : n^3 Polynomial G : (n+1)^2*(2n+1) Z : -1/2 Approximate value : Zeta3_Apery = 1.202056903160