Definition:Meromorphic Function/Definition 2

Definition
Let $U \subset \C$ be an open subset of the complex plane $\C$.

A meromorphic function on $U$ is a complex function that can be expressed as the ratio of two holomorphic functions.

That is:
 * $\map f z = \dfrac {\map g z} {\map h z}$

where:
 * $g: \C \to \C$ and $h: \C \to \C$ are holomorphic
 * $z \in \C$ such that $\map h z \ne 0$

Also see

 * Equivalence of Definitions of Meromorphic Function