wu :: forums « wu :: forums - Summing Infinite Series Using Residue » Welcome, Guest. Please Login or Register. Feb 3rd, 2023, 5:43am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    general    complex analysis (Moderators: william wu, Grimbal, ThudnBlunder, Icarus, Eigenray, towr, SMQ)    Summing Infinite Series Using Residue « Previous topic | Next topic »
 Pages: 1 Reply Notify of replies Send Topic Print
 Author Topic: Summing Infinite Series Using Residue  (Read 10372 times)
MonicaMath
Newbie

Gender:
Posts: 43
 Summing Infinite Series Using Residue   « on: Mar 18th, 2009, 7:43pm » Quote Modify

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
Uberpuzzler

Gender:
Posts: 1321
 Re: Summing Infinite Series Using Residue   « Reply #1 on: Mar 18th, 2009, 10:13pm » Quote Modify