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List of periodic functions

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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.

Smooth functions

All trigonometric functions listed have period , unless otherwise stated. For the following trigonometric functions:

Un is the nth up/down number,
Bn is the nth Bernoulli number
in Jacobi elliptic functions,
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Non-smooth functions

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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)

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Vector-valued functions

Doubly periodic functions

Notes

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