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List of periodic functions

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

Doubly periodic functions

Notes