Residue at Multiple Pole

Theorem
Let $f: \C \to \C$ be a function meromorphic on some region, $D$, containing $a$.

Let $f$ have a pole of order $n$ at $a$.

Then the residue of $f$ at $a$ is given by:


 * $\displaystyle \operatorname{Res} \left({f, a}\right) = \frac 1 {\left({n - 1}\right)!} \lim_{z \mathop \to a} \frac { \d^{n - 1} } { \d z^{n - 1} } \left({\left({z - a}\right)^n f \left({z}\right)}\right)$