Definition:Meromorphic Function

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

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

Then $$f$$ is called a meromorphic function.