This is a list of some well-known periodic functions. The constant function , where is independent of , is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
Smooth functions
All trigonometric functions listed have period , unless otherwise stated. For the following trigonometric functions: is the th up/down number, is the th Bernoulli number in Jacobi elliptic functions,
Non-smooth functions
The following functions have period and take as their argument. The symbol is the floor function of and is the sign function.
K means Elliptic integral K(m)
Vector-valued functions
Epitrochoid
Epicycloid (special case of the epitrochoid) Limaçon (special case of the epitrochoid) Hypotrochoid Hypocycloid (special case of the hypotrochoid) Spirograph (special case of the hypotrochoid)