Holomorphic function

complex functions differentiable everywhere on their domains

In mathematics a holomorphic function is a function that is defined on the complex numbers, and that can be differentiated everywhere where it is defined. Differentiating the function again leads to a function defined on the complex numbers. In older literature, these functions are sometimes called regular.

A rectangular grid is mapped onto its image, using a holomorphic function.

Holomorphic functions show a number of properties function defined on real numbers do not have.