# Definition:Meromorphic Function

## Definition

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

### Definition 1

A meromorphic function on $U$ is a holomorphic function on all of $U$ except for a set of poles of $f$.

### Definition 2

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.

### Definition 3

A meromorphic function on $U$ is a complex function whose only singular points are poles.

## Also see

• Results about meromorphic functions can be found here.