\begin{definition}[Definition:Laurent Series]
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 $U \setminus \set {z_0}$.
{{NamedforDef|Pierre Alphonse Laurent|cat = Laurent}}
\end{definition}