## Franklin's Notes

### Meromorphic function

A meromorphic function is a function $f:\mathbb C\to\mathbb C$ which is holomorphic in some region $\Omega$ except at a set of isolated points in $\mathbb C$, at which it has poles. Equivalently, a meromorphic function $f$ is a function which can be written as a quotient of two holomorphic functions $g,h$ with $h$ not equal to the zero function. The fact that these two definitions are equivalent follows from the fact that holomorphic functions are analytic and the zeros of analytic functions are always isolated.