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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.
The concept of an entire function was of particular interest to Karl Weierstrass during his work on rebuilding the discipline of complex analysis.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): entire function