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.
See also
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.
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Cite this as:
Weisstein, Eric W. "Entire Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EntireFunction.html