FourierCosSeries

FourierCosSeries[expr,t,n]

gives the n-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 -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 \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define Fourier cosine series GenerateConditions False whether 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-order Fourier cosine series of :

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

Scope(3)

Find the -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_2024_fouriercosseries, author="Wolfram Research", title="{FourierCosSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierCosSeries.html}", note=[Accessed: 24-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_fouriercosseries, organization={Wolfram Research}, title={FourierCosSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierCosSeries.html}, note=[Accessed: 24-July-2024 ]}