Meromorphic function

In the mathematical field of complex analysis, a meromorphic function on an open subset ${\displaystyle D}$ of the complex plane is a function that is holomorphic on all of ${\displaystyle D}$ except for a set of isolated points, which are poles of the function. The term comes from the Greek meros (μέρος), meaning 'part'.

Every meromorphic function on ${\displaystyle D}$ can be expressed as the ratio between two holomorphic functions (with the denominator not constant 0) defined on ${\displaystyle D}$: any pole must coincide with a zero of the denominator.