# Contour integral - falls into all exceptions to rules!

1. Sep 1, 2008

### zombiegirl

Hi, I wa swondeirng whether there was a method of performing a particular integral I have to do.

It looks like a contour integral, but it seems to fall into the category of exceptions to every rule I've come across, I don't want to try and write it out on here, but it has the following properties:

* It's a trig funtion integrate dover 2pi (so if you map it into the complex plane you end up with an integral over a unit circle)

* It's not well defined at the origin (but it IS bounded, i.e. it doesn't blow up)

* It has poles ON the unit circle

* If you try to distort the contour at the poles you have the following problems:

- The integral isn't over infinity, so the poles don't lie on what would otherwise be a straight line, they're on the circle. As a result, it's difficult the try and split up the contour into intrable parts (i.e. you'd need to intgrate the function over the arcs).

- When you try to substitute z= R+n*exp[i*phi], then let n (the radius of the distortion around the pole) tend to zero, the entire integrand tends to zero too.

Does anybody have any idea how to deal with such an integral?
I feel as though I've tried absolutely everything!