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Inside-Outside Theorem

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

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

where Res are the Residues.




© 1996-9 Eric W. Weisstein
1999-05-26