Cauchy's integral formula more then one pole? Cauchy's integral formula says that:
$$f(z_0)=\frac{1}{2\pi i}\oint_\Gamma \frac{f(z)}{(z-z_0)}dz$$
Where $\Gamma$ is a closed contour in the positive sense. Does this still hold if $\Gamma$ contains more poles (other then that at $z_0$) of the function $ \frac{f(z)}{(z-z_0)}$?

The version of this for more than one pole inside a contour is called The Residue Theorem
