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A tough integral

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

    Hey guys.

    I have this problem:

    http://img12.imageshack.us/img12/6729/91881544.jpg [Broken]

    It's like a two parts problem.
    The first one was to prove the equation in red, I did that with a bit of trigo.
    The second part is to use the integral of the function in green to prove the thing in yellow. I'm stuck on the path that goes from - epsilon to epsilon, that semi circle, how can I find the value of this function on the path?


    2. Relevant equations

    3. The attempt at a solution
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 10, 2009 #2
    Compute the http://en.wikipedia.org/wiki/Residue_(complex_analysis)" [Broken] of f at zero, the use

    [tex]2\pi iRes(f,0)=\int_{|z|=\epsilon}f(z)dz[/tex]

    and try to find the integral over the half-circle in terms of the integral over the entire circle.
    Last edited by a moderator: May 4, 2017
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