antiperiodic function

A special case of the quasiperiodicity ( of functionsMathworldPlanetmath is the antiperiodicity. An antiperiodic function f satisfies for a certain constant p the equation


for all values of the variable z.  The constant p is the antiperiod of f. Then, f has also other antiperiods, e.g. -p, and generally (2n+1)p with any  n.

The antiperiodic function f is always as well periodic with period 2p, since


Naturally, then there are all periods 2np with  n.

Not all periodic functionsMathworldPlanetmath are antiperiodic.

For example, the sine and cosine functions are antiperiodic with  p=π, which is their absolutely least antiperiod:


The tangent ( and cotangent functions are not antiperiodic although they are periodic (with the prime period π; see complex tangent and cotangent).

The exponential functionDlmfDlmfMathworldPlanetmathPlanetmath is antiperiodic with the antiperiod iπ (see Euler relation):

Title antiperiodic function
Canonical name AntiperiodicFunction
Date of creation 2015-12-16 15:19:14
Last modified on 2015-12-16 15:19:14
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 12
Author pahio (2872)
Entry type Definition
Classification msc 30A99
Related topic PeriodicFunctions
Related topic QuasiperiodicFunction
Defines antiperiodicity
Defines antiperiodic
Defines antiperiod