Definition:Entire Function
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Definition
Let $f: \C \to \C$ be a complex function.
Then:
- $f$ is an entire function
- $f$ is holomorphic over the whole of $\C$.
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
- Results about entire functions can be found here.
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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): entire function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): entire function
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): entire function