Here's the problem:

The function f(z) is holomorphic everywhere on a closed contour $\displaystyle \Gamma$, and also within $\displaystyle \Gamma$ except at a finite set of points where f has poles.

(Recall that a pole of order n at $\displaystyle z = \alpha$ occurs where f(z) is of the form $\displaystyle \frac{h(z)}{(z - \alpha)^n}$, where h(z) is regular at $\displaystyle \alpha$).

Show that:

$\displaystyle \oint_r f(z)dz = 2\pi i*\{\text{sum of the residues at these poles}\}$,

where the residue at the pole $\displaystyle \alpha$ is $\displaystyle \frac{h^{(n-1)}(\alpha)}{(n-1)!}$.

Any and all help is appreciated.