Laurent Expansion of Function about Pole

Theorem
Let $f$ be a complex function with a pole at $z_0 \in \C$ of order $k$.

The Laurent expansion of $f$ about $z_0$ can be expressed as:


 * $\map f z = \ds \sum_{n \mathop = -k}^\infty a_n \paren {z - z_0}^n$