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.

Also see

• Complex Function is Entire iff it has Everywhere Convergent Power Series

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): entire function