FourierSeries

FourierSeries[expr,t,n]

gives the n^(th)-order Fourier series expansion of expr in t.

FourierSeries[expr,{t1,t2,…},{n1,n2,…}]

gives the multidimensional Fourier series.

Details and Options

  • The ^(th)-order Fourier series of is by default defined to be with .
  • The multidimensional Fourier series of is given by with .
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    FourierParameters {1,1}parameters to define Fourier series
    GenerateConditionsFalsewhether to generate results that involve conditions on parameters
  • Common settings for FourierParameters include:
  • {1,1}
    {1,–2Pi}
    {a,b}

Examples

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Basic Examples  (2)

Find the 3^(rd)-order Fourier series of :

Compute an order {2,2} Fourier series:

Scope  (4)

Find the 3^(rd)-order Fourier series of an exponential function:

Fourier series for a Gaussian function:

Fourier series for Abs:

Fourier series for a basis function has only one term:

Options  (1)

FourierParameters  (1)

Use a nondefault setting for FourierParameters:

Wolfram Research (2008), FourierSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierSeries.html.

Text

Wolfram Research (2008), FourierSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierSeries.html.

CMS

Wolfram Language. 2008. "FourierSeries." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FourierSeries.html.

APA

Wolfram Language. (2008). FourierSeries. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FourierSeries.html

BibTeX

@misc{reference.wolfram_2025_fourierseries, author="Wolfram Research", title="{FourierSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierSeries.html}", note=[Accessed: 24-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_fourierseries, organization={Wolfram Research}, title={FourierSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierSeries.html}, note=[Accessed: 24-April-2025 ]}