Definition:Meromorphic Function

Definition

Let $f: \C \to \C$ be a complex function that can be expressed as the ratio of two holomorphic functions.

That is, let $f \left({z}\right) = \dfrac {g \left({z}\right)} {h \left({z}\right)}$, where $g: \C \to \C$ and $h: \C \to \C$ are holomorphic.

Then $f$ is called a meromorphic function.