# FourierSeries

FourierSeries[expr,t,n]

gives the n-order Fourier series expansion of expr in t.

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

gives the multidimensional Fourier series.

# Details and Options

• The -order Fourier series of is by default defined to be with .
• The multidimensional Fourier series of is given by with .
• 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
• Common settings for FourierParameters include:
•  {1,1} {1,–2Pi} {a,b}

# Examples

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## Basic Examples(2)

Find the 3-order Fourier series of :

Compute an order {2,2} Fourier series:

## Scope(4)

Find the 3-order Fourier series of an exponential function:

Fourier series for a Gaussian function:

Fourier series for Abs:

Fourier series for a basis function has only one term:

## Options(1)

### FourierParameters(1)

Use a nondefault setting for FourierParameters:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_fourierseries, author="Wolfram Research", title="{FourierSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierSeries.html}", note=[Accessed: 29-May-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_fourierseries, organization={Wolfram Research}, title={FourierSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierSeries.html}, note=[Accessed: 29-May-2023 ]}