Meromorphic function

A meromorphic function is a function that is holomorphic (defined on the complex numbers, and that can be differentiated everywhere where it is defined) on all of an open set except for a set of isolated points, which are poles of the function.

All rational functions, for example[math]\displaystyle{ f(z) = \frac{z^3 - 2z + 10}{z^5 + 3z - 1}, }[/math]are meromorphic on the whole complex plane.