Holomorhpic function (also known as Analytic function) usually refer to functions that are inifinitely differentiable.

Formal Definition:

Let G be an open set in $C$. A function $f:G→C$ is called holomorphic if, at every point $z∈G$, the complex derivative

$f_{′}(z)=h→0lim hf(z+h)−f(z) $

exists as a complex number where $C$ = complex realm.

## Meromorphic Functions

Meromorphic Function is the ratio of two analytic function which are analytic except for isolated singularities.

## What it means to be complex differentiable

Difference between regular differentiable vs complex differentiable.