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Periodic Function


A Function $f(x)$ is said to be periodic with period $p$ if $f(x)=f(x+np)$ for $n=1$, 2, .... For example, the Sine function $\sin x$ is periodic with period $2\pi$ (as well as with period $-2\pi$, $4\pi$, $6\pi$, etc.).

The Constant Function $f(x)=0$ is periodic with any period $R$ for all Nonzero Real Numbers $R$, so there is no concept analogous to the Least Period or a Periodic Point for constant functions.

See also Periodic Point, Periodic Sequence


Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 425-427, 1953.

Spanier, J. and Oldham, K. B. ``Periodic Functions.'' Ch. 36 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 343-349, 1987.

© 1996-9 Eric W. Weisstein