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 :

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

Scope  (3)

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

Fourier cosine series for a piecewise function:

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

Options  (1)

FourierParameters  (1)

Use a nondefault setting for FourierParameters:

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_2025_fouriercosseries, author="Wolfram Research", title="{FourierCosSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierCosSeries.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_fouriercosseries, organization={Wolfram Research}, title={FourierCosSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierCosSeries.html}, note=[Accessed: 22-February-2025 ]}