Antiperiodic Function

A function is said to be antiperiodic with antiperiod if

for , 3, .... For example, the sine function is antiperiodic with period (as well as with antiperiods , , etc.).

It can be easily shown that if is antiperiodic with period , then it is periodic with period . But if is periodic with period , may or may not be antiperiodic with period .

The constant function has the interesting property of being periodic with any period and antiperiodic with any antiperiod for all nonzero real numbers .