Periodic Function -- From Wolfram MathWorld

Home » What Does Periodic Mean In Calculus » Periodic Function -- From Wolfram MathWorld

Maybe your like

Search Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
  • Calculus and Analysis
  • Functions
  • MathWorld Contributors
  • Lambrou
Periodic Function DOWNLOAD Mathematica NotebookDownload Wolfram Notebook PeriodicFunction

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if

f(x)=f(x+np)

for n=1, 2, .... For example, the sine function sinx, illustrated above, is periodic with least period (often simply called "the" period) 2pi (as well as with period -2pi, 4pi, 6pi, 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 for constant functions. The following table summarizes the names given to periodic functions based on the number of independent periods they possess.

number of periodsname
1singly periodic function
2doubly periodic function
3triply periodic function

See also

Almost Periodic Function, Antiperiodic Function, Doubly Periodic Function, Least Period, Period, Periodic Point, Periodic Sequence, Singly Periodic Function, Triply Periodic Function

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

  • absolute value
  • functions
  • period of sin(3t)

References

Knopp, K. "Periodic Functions." Ch. 3 in Theory of Functions Parts I and II, Two Volumes Bound as One, Part II. New York: Dover, pp. 58-92, 1996.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.

Referenced on Wolfram|Alpha

Periodic Function

Cite this as:

Weisstein, Eric W. "Periodic Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PeriodicFunction.html

Subject classifications

  • Calculus and Analysis
  • Functions
  • MathWorld Contributors
  • Lambrou
Created, developed and nurtured by Eric Weisstein at Wolfram Research

Tag » What Does Periodic Mean In Calculus