# FourierTrigSeries

FourierTrigSeries[expr,t,n]

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

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

gives the multidimensional Fourier trigonometric series of expr.

# Details and Options

• The n-order Fourier trigonometric series of is by default defined to be with and .
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define Fourier trig series GenerateConditions False whether to generate results that involve conditions on parameters
• With the setting FourierParameters->{a,b} the following series is returned: with and .

# Examples

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## Basic Examples(2)

Find the 5-order Fourier trigonometric series of t:

Find the 3-order bivariate Fourier trigonometric series approximation to :

## Scope(4)

Find the Fourier trigonometric series of an exponential function:

Fourier trigonometric series for a Gaussian function:

Fourier trigonometric series for Abs:

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

## Options(1)

### FourierParameters(1)

Use a nondefault setting for:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_fouriertrigseries, author="Wolfram Research", title="{FourierTrigSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierTrigSeries.html}", note=[Accessed: 28-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_fouriertrigseries, organization={Wolfram Research}, title={FourierTrigSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierTrigSeries.html}, note=[Accessed: 28-September-2023 ]}