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

Formal Definition:

Let G be an open set in . A function is called holomorphic if, at every point , the complex derivative

exists as a complex number where = 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.