# FourierCosCoefficient

FourierCosCoefficient[expr,t,n]

gives the n coefficient in the Fourier cosine series expansion of expr.

FourierCosCoefficient[expr,{t1,t2,},{n1,n2,}]

gives a multidimensional Fourier cosine coefficient.

# Details and Options

• The coefficient in the Fourier cosine series expansion of is by default given by .
• The dimensional Fourier cosine coefficient is given by .
• In the form FourierCosCoefficient[expr,t,n], n can be symbolic or a nonnegative integer.
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define Fourier series GenerateConditions False whether to generate results that involve conditions on parameters
• The function expr is assumed to be periodic in t with period , except when otherwise specified by FourierParameters.
• Common settings for FourierParameters include:
•  {1,1} default settings {1,2Pi} period 1 {a,b} general setting

# Examples

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## Basic Examples(2)

Find the 5 Fourier cosine coefficient:

Find the general term coefficient:

Plot the sequence:

Find the {3,5} Fourier cosine coefficient:

Find the coefficient of the general term:

Plot the multivariate sequence:

## Scope(4)

Find the 6 Fourier cosine coefficient for a quadratic polynomial:

General Fourier cosine coefficient for a piecewise function:

Fourier cosine coefficient for a Gaussian function:

Fourier cosine coefficient for a basis function:

## Options(1)

### FourierParameters(1)

Use a nondefault setting for FourierParameters:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_fouriercoscoefficient, author="Wolfram Research", title="{FourierCosCoefficient}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierCosCoefficient.html}", note=[Accessed: 30-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_fouriercoscoefficient, organization={Wolfram Research}, title={FourierCosCoefficient}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierCosCoefficient.html}, note=[Accessed: 30-September-2023 ]}