# Homework Help: Proof of integral identity (popped up in a Fourier transform)

1. Oct 3, 2011

### phagist_

1. The problem statement, all variables and given/known data

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

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. Oct 4, 2011

### phagist_

any ideas? I am legitimately stumped on this one..