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   Summing Infinite Series Using Residue
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   Author  Topic: Summing Infinite Series Using Residue  (Read 10296 times)
MonicaMath
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Summing Infinite Series Using Residue  
« on: Mar 18th, 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 18th, 2009, 7:45pm by MonicaMath » IP Logged
Aryabhatta
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Re: Summing Infinite Series Using Residue  
« Reply #1 on: Mar 18th, 2009, 10:13pm »
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Can you show your working?
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