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# Entire Function

If a complex function is analytic at all finite points of the complex plane , then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112).

Any polynomial is entire.

Examples of specific entire functions are given in the following table.

Liouville's boundedness theorem states that a bounded entire function must be a constant function.

Analytic Function, Finite Order, Hadamard Factorization Theorem, Holomorphic Function, Liouville's Boundedness Theorem, Meromorphic Function, Weierstrass Product Theorem

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## References

Knopp, K. "Entire Transcendental Functions." Ch. 9 in Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, pp. 112-116, 1996.Krantz, S. G. "Entire Functions and Liouville's Theorem." §3.1.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 31-32, 1999.

Entire Function

## Cite this as:

Weisstein, Eric W. "Entire Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EntireFunction.html