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Proof of integral identity (popped up in a Fourier transform)

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove;
    [itex]\int_{-\infty}^{\infty} \frac{sin(\gamma)}{cosh(\lambda)-cos(\gamma)} e^{i \omega \lambda}d \lambda= 2 \pi \frac{sinh(\omega(\pi-\gamma))}{sinh(\pi \omega)}[/itex]

    2. Relevant equations

    Contour Integration/Residue Theorem?

    3. The attempt at a solution
    I have messed around with the exponential for a bit, but to no avail - I was thinking maybe the Residue theorem might play a part? I'm not really sure how to continue from here.
     
  2. jcsd
  3. Oct 4, 2011 #2
    any ideas? I am legitimately stumped on this one..
     
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