FourierSinSeries

FourierSinSeries[expr,t,n]

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

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

gives the multidimensional Fourier sine series of expr.

Details and Options

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

Examples

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Basic Examples  (2)

Find the 5^(th)-order Fourier sine series approximation to t:

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

Scope  (3)

Find the 3^(rd)-order Fourier sine series approximation to a quadratic polynomial:

Fourier sine series for a piecewise function:

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

Options  (1)

FourierParameters  (1)

Use a nondefault setting for FourierParameters:

Properties & Relations  (1)

The Fourier sine series of :

The Fourier series of the odd extension of :

In general these will always coincide:

The Fourier sine series of approximates :

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_fouriersinseries, author="Wolfram Research", title="{FourierSinSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierSinSeries.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_fouriersinseries, organization={Wolfram Research}, title={FourierSinSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierSinSeries.html}, note=[Accessed: 21-February-2025 ]}