Definition:Meromorphic Function

Definition
Let $U \subset \C$ be an open set.

A meromorphic function on $U$ is a holomorphic function on the complement of a discrete subset $P \subset U$ such that:
 * for all $p\in P$, $f$ has either a pole or removable singularity at $p$.

Also see

 * Definition:Holomorphic Function
 * Meromorphic Function is Quotient of Holomorphic Functions