Movatterモバイル変換

[0]ホーム
URL:

WOLFRAM

Wolfram Language & System Documentation Center
FunctionPeriod

FunctionPeriod[f,x]

gives a periodp of the functionf over the reals such that.

FunctionPeriod[f,x,dom]

gives a period withx restricted to the domaindom.

FunctionPeriod[{f1,f2,…},{x1,x2,…},…]

gives periods{p1,p2,…} for{x1,x2,…} such that.

Details
Details and OptionsDetails and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Periodic Functions over the Integers  
See Also
Related Guides
History
Cite this Page

FunctionPeriod

FunctionPeriod[f,x]

gives a periodp of the functionf over the reals such that.

FunctionPeriod[f,x,dom]

gives a period withx restricted to the domaindom.

FunctionPeriod[{f1,f2,…},{x1,x2,…},…]

gives periods{p1,p2,…} for{x1,x2,…} such that.

Details

  • A periodp is taken to be zero if no period can be found.
  • Possible domainsdom areReals,Integers, andComplexes.
  • Periods over theComplexes are given in a list and can consist of one or two complex periods.

Examples

open allclose all

Basic Examples  (3)

Find a period of the sine function:

Plot of two complete periods:

Find a period of a sequence:

Plot the sequence:

Find periods for multidimensional functions:

Plot the contours:

Scope  (9)

Basic Uses  (4)

Find periods over integers:

Find periods over reals:

Find periods over complexes:

Periods of functions with parameters:

Periodic Functions over the Integers  (5)

Basic periodic sequences includeMod:

Mod of a polynomial:

The function:

And in general powers of roots of unity, i.e. roots of the polynomial:

A common way to express these are:

Trigonometric functions with a rational multiple of their real period:

A function where is periodic over the reals with period and rational:

It works similarly for a function periodic over the complexes:

Any finite sum of periodic sequences is periodic:

Any finite product of periodic sequences is periodic:

Any function combination of periodic sequences is periodic:

See Also

FunctionDomain FunctionRange DifferenceDelta Differences FourierSeries FindRepeat FindTransientRepeat

Function Repository:FunctionPeriodPlot FunctionOverview

Related Guides

History

Introduced in 2014(10.0)

Wolfram Research (2014), FunctionPeriod, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionPeriod.html.

Text

Wolfram Research (2014), FunctionPeriod, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionPeriod.html.

CMS

Wolfram Language. 2014. "FunctionPeriod." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FunctionPeriod.html.

APA

Wolfram Language. (2014). FunctionPeriod. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionPeriod.html

BibTeX

@misc{reference.wolfram_2025_functionperiod, author="Wolfram Research", title="{FunctionPeriod}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/FunctionPeriod.html}", note=[Accessed: 29-November-2025]}

BibLaTeX

@online{reference.wolfram_2025_functionperiod, organization={Wolfram Research}, title={FunctionPeriod}, year={2014}, url={https://reference.wolfram.com/language/ref/FunctionPeriod.html}, note=[Accessed: 29-November-2025]}

Top
[8]ページ先頭
©2009-2025 Movatter.jp