Meromorphic functions are complex-valued functions which are holomorphic everywhere on an open domain except a set of isolated points which are poles. Consider also using the (complex-analysis) tag.
Meromorphic functions are complex-valued functions which are holomorphic everywhere on an open domain except a set of isolated points which are poles. The quotient of two holomorphic functions $f$ and $g$ defined on a domain $D$, where $g$ is not the null function, is a meromorphic function and every meromorphic function defined on $D$ can be expressed as the quotient of two holomorphic functions. Therefore, the relationship between holomorphic functions and meromorphic functions defined on $D$ is similar to the relationship between the integers and the rational numbers.
