# Simply-periodic function

From Encyclopedia of Mathematics

*simple periodic function*

A periodic function of the complex variable all periods of which are integer multiples of a single unique fundamental, or primitive, period , i.e. (). For example, the exponential function is an entire simply-periodic function with fundamental period , and the trigonometric functions and are meromorphic simply-periodic functions with fundamental period .

#### Comments

More generally, a simply-periodic function on a linear space is a periodic function whose periods are integer multiples of some basic period . A non-constant continuous periodic function of a real variable is necessarily simply-periodic.

**How to Cite This Entry:**

Simply-periodic function.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Simply-periodic_function&oldid=11772

This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article