# Homework Help: An analytic solution for a fourier transform

1. Mar 9, 2014

### jtceleron

1. The problem statement, all variables and given/known data
the function is Exp[-w^2]/w^2, how to solve the Fourier transform analytically with Residue theorem?
It is better if there is more general results.
Mathematica can solve it analytically, but I need a human-soluable way.

2. Relevant equations

3. The attempt at a solution
My attempt follows the Fresnel integral, but there is still something wrong.

2. Mar 10, 2014

### vanhees71

The integral is undefined as it stands, because there's the pole at $\omega=0$. You have to specify how to run around this pole first!