FourierTrigSeries

FourierTrigSeries[expr,t,n]

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

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

gives the multidimensional Fourier trigonometric series of expr.

Details and Options

  • The n^(th)-order Fourier trigonometric series of is by default defined to be with and .
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    FourierParameters {1,1}parameters to define Fourier trig series
    GenerateConditionsFalsewhether to generate results that involve conditions on parameters
  • With the setting FourierParameters->{a,b} the following series is returned: with and .

Examples

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Basic Examples  (2)

Find the 5^(th)-order Fourier trigonometric series of t:

Find the 3^(rd)-order bivariate Fourier trigonometric series approximation to :

Scope  (4)

Find the Fourier trigonometric series of an exponential function:

Fourier trigonometric series for a Gaussian function:

Fourier trigonometric series for Abs:

The Fourier trigonometric series for a basis function has only one term:

Options  (1)

FourierParameters  (1)

Use a nondefault setting for FourierParameters:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_fouriertrigseries, author="Wolfram Research", title="{FourierTrigSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierTrigSeries.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_fouriertrigseries, organization={Wolfram Research}, title={FourierTrigSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierTrigSeries.html}, note=[Accessed: 22-February-2025 ]}