# Having trouble evaluating an integral

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:

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quasar987
Homework Helper
Gold Member
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.

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 :)