# Definition:Entire Function

## Definition

A holomorphic self-map $f$ of the complex plane is called an entire function.

### Transcendental Entire Function

Let $f$ be an entire function that has an essential singularity at $\infty$.

Then $f$ is a transcendental entire function.

## Historical Note

The concept of an entire function was of particular interest to Karl Weierstrass during his work on rebuilding the discipline of complex analysis.