If a complex function is analytic at all finite points of the complex plane
Any polynomial
Examples of specific entire functions are given in the following table.
function symbol Airy functions Airy function derivatives Anger function Barnes
G-function bei ber Bessel
function of the first kind Bessel
function of the second kind Beurling's
function cosine coversine Dawson's integral erf erfc erfi exponential
function Fresnel
integrals gamma
function reciprocalgeneralized
hypergeometric function haversine hyperbolic
cosine hyperbolic
sine Jacobi
elliptic functions Jacobi
theta functions Jacobi theta
function derivatives Mittag-Leffler
function modified
Struve function Neville
theta functions Shi sine sine integral spherical
Bessel function of the first kind Struve
function versine Weber functions Wright function xi-function
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
Explore with Wolfram|Alpha
References Knopp, K. "Entire Transcendental Functions." Ch. 9 in Theory
of Functions Parts I and II, Two Volumes Bound as One, Part I. Krantz, S. G. "Entire Functions
and Liouville's Theorem." §3.1.3 in Handbook
of Complex Variables. Referenced
on Wolfram|Alpha Entire Function
Cite this as:
Weisstein, Eric W. "Entire Function."
From MathWorld https://mathworld.wolfram.com/EntireFunction.html
Subject classifications More... Less...
, then it is said to be entire, sometimes also called "integral"
(Knopp 1996, p. 112).
is entire.
, 
,
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
