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=31936
Simply-periodic function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simply-periodic_function&oldid=31936
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article