MathGroup Archive 2001

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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])=



Subject: [mg30216]      serie
Author:       Ahmet Mutlu <ahmet at>
Organization: Steven M. Christensen and Associates, Inc and
MathTensor, Inc.

what is the sum

for i:=1 to k
    total = total + 1/(i^2 + 1)

i mean, a formal sum.

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