Antiperiodic Function

A function f(x) is said to be antiperiodic with antiperiod p if

for n=1, 3, .... For example, the sine function sinx is antiperiodic with period pi (as well as with antiperiods 3pi, 5pi, etc.).

It can be easily shown that if f(x) is antiperiodic with period p, then it is periodic with period 2p. But if f(x) is periodic with period 2p, f(x) may or may not be antiperiodic with period p.

The constant function f(x)=0 has the interesting property of being periodic with any period R and antiperiodic with any antiperiod R for all nonzero real numbers R.

See also

This entry contributed by Giorgi Dalakishvili

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Dalakishvili, Giorgi. "Antiperiodic Function." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AntiperiodicFunction.html

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