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Residue theorem

  1. Feb 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Hey guys.
    So I got this integral I need to solve, of curse using the residue theorem.
    The thing is, that I don't understand the curve.
    I know that whenever Z^2 = integer, this function has a singularity point because e^(2*pi*i*n) = 1.
    But again, I'm not sure what this curve has enclosed in.

    Thanks.

    2. Relevant equations



    3. The attempt at a solution
     

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  3. Feb 10, 2009 #2

    HallsofIvy

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    This is, actually, an "infinite sequence" of problems! Each path is a circle, with center (0,0) of radius R which lies between [itex]\sqrt{n}[/itex] and [itex]\sqrt{n+1}[/itex] for each positive integer n. I suspect that you will find that the number of poles inside each path depends on n.
     
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