FourierSinCoefficient

FourierSinCoefficient[expr,t,n]

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

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

gives a multidimensional Fourier sine coefficient.

Details and Options

• The coefficient in the Fourier sine series expansion of is by default given by .
• The -dimensional Fourier sine coefficient is given by .
• In the form FourierSinCoefficient[expr,t,n], n can be symbolic or a positive 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

open allclose all

Basic Examples(2)

Find the 3 Fourier sine series coefficient:

Find the general term coefficient:

Plot the coefficient sequence:

Find the {3,5} Fourier sine coefficient:

The general term:

Plot the coefficient sequence:

Scope(4)

Find the 5 Fourier sine coefficient for a quadratic polynomial:

Find the general coefficient for a piecewise function:

General Fourier sine coefficient for a Gaussian function:

Fourier sine coefficient for a basis function:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2023_fouriersincoefficient, author="Wolfram Research", title="{FourierSinCoefficient}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierSinCoefficient.html}", note=[Accessed: 30-September-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_fouriersincoefficient, organization={Wolfram Research}, title={FourierSinCoefficient}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierSinCoefficient.html}, note=[Accessed: 30-September-2023 ]}