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FourierCosSeries[expr,t,n]

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

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

gives the multidimensional Fourier cosine series of expr.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
FourierParameters  
See Also
Related Guides
History
Cite this Page

FourierCosSeries

FourierCosSeries[expr,t,n]

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

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

gives the multidimensional Fourier cosine series of expr.

Details and Options

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

Examples

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Basic Examples  (2)

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

Wolfram Language code: FourierCosSeries[t ^ 2, t, 5]
Wolfram Language code: Plot[%, {t, -3Pi, 3Pi}]

Find the {2,2}-order Fourier cosine series:

Wolfram Language code: FourierCosSeries[x Exp[-y], {x, y}, {2, 2}]
Wolfram Language code: Plot3D[%, {x, -Pi, Pi}, {y, -Pi, Pi}]

Scope  (3)

Find the 4^(th)-order Fourier cosine series of a quadratic polynomial:

Wolfram Language code: FourierCosSeries[t ^ 2 + 3t + 7, t, 4]

Fourier cosine series for a piecewise function:

Wolfram Language code: FourierCosSeries[UnitStep[t(Pi / 2 - t)], t, 10]
Wolfram Language code: Plot[%, {t, 0, Pi}]

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

Wolfram Language code: FourierCosSeries[Cos[3 t], t, 5]

Options  (1)

FourierParameters  (1)

Use a nondefault setting for FourierParameters:

Wolfram Language code: FourierCosSeries[UnitStep[t(1 / 4 - t)], t, 10, FourierParameters -> {1, 2Pi}]
Wolfram Language code: Plot[%, {t, 0, 1 / 2}]
Wolfram Research (2008), FourierCosSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierCosSeries.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_fouriercosseries, author="Wolfram Research", title="{FourierCosSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierCosSeries.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_fouriercosseries, organization={Wolfram Research}, title={FourierCosSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierCosSeries.html}, note=[Accessed: 12-June-2026]}