# Definition:Entire Function

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## 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**.

## Also see

## 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.

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**entire function**