List of periodic functions

This list is incomplete; you can help by expanding it.

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.

Real-valued functions

Trigonometric functions

• Sine
• Cosine
• Tangent

Sinus-like functions

• Trochoid
• Cycloid
• Clausen function

Non-smooth functions

• Triangle wave (non-continuous first derivative)
• Sawtooth wave (non-continuous)
• Square wave (non-continuous)
• Cycloid (non-continuous first derivative)
• Tangent (non-continuous)

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)

Complex-valued functions

• Euler's formula, e^ix = cos x + i sin x, as a function of x