Residue at Simple Pole

Theorem
Let $f: \C \to \C$ be a complex function with a simple pole at $a \in \C$.

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


 * $\displaystyle \operatorname{Res} \left({f, a}\right) = \lim_{z \mathop \to a} \left({z - a}\right) f \left({z}\right)$