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Topic: Summing Infinite Series Using Residue (Read 10296 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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Aryabhatta
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Re: Summing Infinite Series Using Residue
« Reply #1 on: Mar 18^{th}, 2009, 10:13pm » 
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Can you show your working?


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