Definition:Laurent Series

Definition
Let $f: \C \to \C$ be a complex function.

Let $z_0 \in U \subset \C$ such that $f$ is analytic in $U \setminus \set {z_0}$.

A Laurent series is a summation:
 * $\ds \sum_{j \mathop = -\infty}^\infty a_j \paren {z - z_0}^j$

such that the summation converges to $f$ in $U \setminus \set {z_0}$.

Also known as
A Laurent series is also commonly known as a Laurent expansion.