# FourierSinSeries

FourierSinSeries[expr,t,n]

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

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

gives the multidimensional Fourier sine series of expr.

# Details and Options

• The -order Fourier sine series of is by default defined to be with .
• The -dimensional Fourier sine series of is given by with .
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define Fourier sine 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 sine series of is equivalent to the Fourier series of .

# Examples

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## Basic Examples(2)

Find the 5-order Fourier sine series approximation to t:

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

## Scope(3)

Find the 3-order Fourier sine series approximation to a quadratic polynomial:

Fourier sine series for a piecewise function:

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

## Options(1)

### FourierParameters(1)

Use a nondefault setting for :

## Properties & Relations(1)

The Fourier sine series of :

The Fourier series of the odd extension of :

In general these will always coincide:

The Fourier sine series of approximates :

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2022_fouriersinseries, author="Wolfram Research", title="{FourierSinSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierSinSeries.html}", note=[Accessed: 27-March-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_fouriersinseries, organization={Wolfram Research}, title={FourierSinSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierSinSeries.html}, note=[Accessed: 27-March-2023 ]}