Liouville's theorem: Difference between revisions

From Companal
(New page: ==Statement== Any entire function (holomorphic function on the whole of <math>\mathbb{C}</math>) that is bounded (i.e. its image is bounded in absolute value) must be constant. ==Fac...)
 
No edit summary
Line 1: Line 1:
{{basic fact}}
==Statement==
==Statement==



Revision as of 18:37, 26 April 2008

This article gives the statement, and possibly proof, of a basic fact in complex analysis.
View a complete list of basic facts in complex analysis

Statement

Any entire function (holomorphic function on the whole of ) that is bounded (i.e. its image is bounded in absolute value) must be constant.

Facts used

Proof