Fourier analysis of a Lorentzian/Cauchy/Breit–Wigner distribution

[nf405]

So I'm supposed to do this but is it just me or is it too hard to do this analytically? (I put it into wolfram online integrator and he couldn't do it) I don't need it very accurate so are there any approximations to this distribution that I could use to make it easier? Anyone have any ideas of a clever way of doing this?

see http://mathworld.wolfram.com/CauchyDistribution.html

for the Cauchy distribution and

http://en.wikipedia.org/wiki/Fourier_analysis

for Fourier analysis if you can't remember the formula

I've never done any numerical integration so if that's the only way I have to learn how to do that from scratch so any clever tricks I could use to avoid that would be appreciated.

 

[Pere Callahan]

I suggest using the calculus of residues.