Periodic function :

A function is said to be periodic(or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with a period if , where .

For example, the sine function , illustrated above, is periodic with least period(often simply called " the " period) (as well as with period - , , , etc.).

The constant function is periodic with any period for all nonzero real numbers , so there is no concept analogous to the least period for constant functions.

The following table summarizes the names given to periodic functions based on the number of independent periods they posses.

Number of periods	Name
	Singly periodic function
	Doubly periodic function
	Triply periodic function

A function is said to be periodic(or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with a period if , where .