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general >> complex analysis >> Summing Infinite Series Using Residue
(Message started by: MonicaMath on Mar 18th, 2009, 7:43pm)

Title: Summing Infinite Series Using Residue
Post by MonicaMath on Mar 18th, 2009, 7:43pm
if we want to sum an infinite series like
sum{k=1 to inf} 1/k^2 using residues we can use the residues of H(z)=cot(z)/z^2 , at the poles k*pi , k=1,2,3,..., and Residue of H at z=0 is -1/3, so the sum will be pi^2/6.

How can I sum the doubling series :
sum{k= - inf to inf} (1/k^3 +2)

using residue method, I tried to follow the same technique as above but it is not working !?

could anyone help me...

Thanks

Title: Re: Summing Infinite Series Using Residue
Post by Aryabhatta on Mar 18th, 2009, 10:13pm
Can you show your working?



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