Periodic function

Example of a periodic function, with period $T$. If you choose any point on the function and then move to the left or right by $T$, you will find the same value as at the original point.

In mathematics a periodic function is a function that repeats itself after a while, and indefinitely. The mathematical definition of this is that $f(t)$ is periodic with period $T$ if

$f(t+T)=f(t)\ \ \forall \ t\in \mathbb {R} \ .$

Common examples of periodic functions are $\sin(\omega t)$ and $\cos(\omega t)$, which both have period $2\pi /\omega$.

A sawtooth wave is a periodic function that can be described by

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = \begin{cases} |x-1| & \text{if } -1<x<1, \\ f(x+2) & \text{if } x \le -1, \\ f(x-2) & \text{if } x \ge 1. \end{cases} }