Simply-periodic function

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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 .


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