A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x) = f(x + n p) for n = 1, 2, .... For example, the sine function sin x, illustrated above, is periodic with least period (often simply called "the" period) 2π (as well as with period -2 π, 4π, 6π, etc.). The constant function f(x) = 0 is periodic with any period R for all nonzero real numbers R, 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.

almost periodic function | antiperiodic function | doubly periodic function | least period | period | periodic point | periodic sequence | singly periodic function | triply periodic function