Re:"serie"

*To*: mathgroup at smc.vnet.net*Subject*: [mg30216] Re:"serie"*From*: seidovzf at yahoo.com (Zakir F. Seidov)*Date*: Thu, 2 Aug 2001 03:16:10 -0400 (EDT)*References*: <9k5ql9$h9m$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

At arbitary k this Sum is a function of complex argument: S = 1/2*(1 + Pi*Coth[Pi] - I*(HarmonicNumber[-I + k] - HarmonicNumber[I + k])) With k->Infinity S -> 1/2*(1 + Pi*Coth[Pi])= 2.076674047468581174134050794750000490446. Zak %%%%%%%%%%%%%%%%%%%%%%%%%5 Subject: [mg30216] serie Author: Ahmet Mutlu <ahmet at ata.cs.hun.edu.tr> Organization: Steven M. Christensen and Associates, Inc and MathTensor, Inc. hi what is the sum for i:=1 to k total = total + 1/(i^2 + 1) i mean, a formal sum.