# Complex analysis formula for an integral

1. Sep 28, 2011

### nugget

1. The problem statement, all variables and given/known data

Find a formula for:

$\int$$1/(z-a)m(z-b)n$dz

around a ball of radius R, centred at z0

where |a| < R < |b| and m,n$\in$N.

2. Relevant equations

Not sure which equations to use, a cauchy integral formula maybe...?

3. The attempt at a solution

I've attempted to split the fraction up into partial fractions, so that the integral is now:

$\int$$1/(z-a)m(b-a)n$+$1/(z-b)n(b-a)m$dz

but I don't think this has made it any easier to solve...

any suggestions?

2. Sep 28, 2011

### lanedance

so do you mean
$$\int \frac{1}{(z-a)^m(z-b)^n} dz$$

how about considering poles & residues?