\begin{definition}[Definition:Multiplicity (Complex Analysis)]
Let $f: \C \to \C$ be a function.
Suppose there is $a \in \C$ such that $\map f a = 0$.
Then $a$ is said to be a '''zero of multiplicity $k$''' if there exists non-zero $L \in \R$ such that:
:$\ds \lim_{z \mathop \to a} \dfrac {\cmod {\map f z} } {\cmod {z - a}^k} = L$
{{definition wanted|Needs to be expanded so as to be relevant to other fields, not just $\C$.}}
Category:Definitions/Complex Analysis
\end{definition}