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   Summing Infinite Series Using Residue

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Topic: Summing Infinite Series Using Residue (Read 10622 times)

MonicaMath
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Summing Infinite Series Using Residue
« on: Mar 18^th, 2009, 7:43pm »

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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

« Last Edit: Mar 18^th, 2009, 7:45pm by MonicaMath »

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