Periodic function

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

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}
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