Inside-Outside Theorem

Let $P(z)$ and $Q(z)$ be Polynomials with Complex arguments and ${\rm deg}(Q)\geq{\rm deg}(P+2)$. Then

$$\int_\gamma {P(z)\over Q(z)}\, dz = \cases{ 2\pi i \sum_{{\... ...\rm outside\ }\gamma} {\rm Res}\, f(z) & outside $\gamma$,\cr}$$

where Res are the Residues.