Periodic function

Definition

Let $f \colon \mathbb{R} \to \mathbb{R}$ be a function and let $T$ be a real number. The number $T$ is a period of $f$ if $f(x + T) = f(x)$ for all $x \in \mathbb{R}$ . The function $f$ is periodic if it has a period $T \ne 0$ .

Remarks

If $T$ is a period, then so is $k T$ for each integer $k$ . The sine function is periodic with period $2 \pi$ . If a continuous periodic function is not constant, it has a smallest positive period. The Dirichlet function has every rational number as a period. Mathlib defines periods as Function.Periodic.

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Tag	`089KWVYD69`
URI	`m2://089KWVYD69`
Kind	definition
Writing	W1 stated
MSC	26A09
Defines	Periodic function

Periodic function

Definition

Remarks

Where this leads

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