# Homework Help: Having trouble evaluating an integral

1. Nov 4, 2006

### mcah5

Hello,

I'm trying to find a series expression for the triangle waveform through some messy math.

I've reduced the problem down to solving the integral:

Integrate[ 1/w^2 * (1-Cos[T*w/2]) * Exp[(1-n)*I*t*w ] with respect to w from -Infinity to Infinity

T is a constant, I is Sqrt[-1], and n is an integer.

Mathematica cannot evaluate this integral, but if I use the function InverseFourierTransform and substitute a specific value of n, mathematica works. I plotted for a couple of n's and I know this is the integral I want.

I tried doing the integral through residues, but the only singularity I can see is w = 0 and the residue there is zero.

The problem is Ex. #5 part d of http://www.hep.caltech.edu/~fcp/math/distributions/distributions.pdf (scroll all the way down to the bottom)

Is there some residue I'm not seeing?

Thanks!

Last edited: Nov 4, 2006
2. Nov 4, 2006

### quasar987

Why not simply expand the exp(i[...]) in sin and cos and separate the integral in real and imaginary part and integrate them separately.

Pehaps use the cosAcosB and CosASinB identities on the resulting integrals.

3. Nov 4, 2006

### mcah5

Actually, I just re-read the question. It asks that I find the fourier transform of f, not f itself so I don't need to do this integral

Now I feel stupid. I'll try that method though, thanks :)