List of periodic functions

This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, 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.

All trigonometric functions listed have period ${\displaystyle 2\pi }$, unless otherwise stated. For the following trigonometric functions:

U_n is the nth up/down number,

B_n is the nth Bernoulli number

in Jacobi elliptic functions, ${\displaystyle q=e^{-\pi {\frac {K(1-m)}{K(m)}}}}$

The following functions have period ${\displaystyle p}$and take ${\displaystyle x}$as their argument. The symbol ${\displaystyle \lfloor n\rfloor }$is the floor function of ${\displaystyle n}$and ${\displaystyle \operatorname {sgn} }$is the sign function.

K means Elliptic integral K(m)

• 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)

• Jacobi's elliptic functions
• Weierstrass's elliptic function