# Contour Choosing Problem

1. May 3, 2007

### Mitra

I would like to find this integral analytically by using “Cauchy Residue Theorem”, but my problem is what contour is suitable?

$$\int {\frac {\exp(-M\omega) \exp(iN\omega)} {\omega^5(\frac{\omega^4}{f^4} + \frac{(\omega^2)(4\zeta^2-2)}{f^2}+ 1)}d\omega$$

From 0 to $$\infty$$
Where, M, N,f and $$\zeta$$ are real and positive.

Since the function has a singularity at 0 on the Semi circle Contour, what do you suggest as a contour? A Keyhole Contour? or a semicircle contour with a small detour around 0?

Last edited: May 3, 2007
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