Periodic function
function that repeats its values in regular intervals or periods
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which are used to describe waves and other repeating phenomena, are periodic. Many aspects of the natural world have periodic behavior, such as the phases of the Moon, the swinging of a pendulum, and the beating of a heart.
The length of the interval over which a periodic function repeats is called its period. Any function that is not periodic is called aperiodic.
Definition
A function is defined as periodic if its values repeat at regular intervals. For example, the positions of the hands on a clock display periodic behavior as they cycle through the same positions every 12 hours. This repeating interval is known as the period.
More formally, a function
f
{\displaystyle f}
is periodic if there exists a nonzero constant
P
{\displaystyle P}
such that
f
(
x
+
P
)
=
f
(
x
)
{\displaystyle f(x+P)=f(x)}
for all values of
x
{\displaystyle x}
in the domain. A nonzero constant
P
{\displaystyle P}
for which this condition holds is called a period of the function.
The public source identifies “Periodic function” as function that repeats its values in regular intervals or periods. This brief keeps that definition visible, then builds a research path around Periodic, function and repeats.
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This entry incorporates text from “Periodic function” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.