FourierSinCoefficient
✖
FourierSinCoefficient
gives the n coefficient in the Fourier sine series expansion of expr.
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 allBasic Examples (2)Summary of the most common use cases
Find the 3 Fourier sine series coefficient:

https://wolfram.com/xid/0fq45s5m3luaa-cghf56

Find the general term coefficient:

https://wolfram.com/xid/0fq45s5m3luaa-fr890

Plot the coefficient sequence:

https://wolfram.com/xid/0fq45s5m3luaa-blezrk

Find the {3,5} Fourier sine coefficient:

https://wolfram.com/xid/0fq45s5m3luaa-ky7uzz


https://wolfram.com/xid/0fq45s5m3luaa-wz9lb

Plot the coefficient sequence:

https://wolfram.com/xid/0fq45s5m3luaa-dskp53

Scope (4)Survey of the scope of standard use cases
Find the 5 Fourier sine coefficient for a quadratic polynomial:

https://wolfram.com/xid/0fq45s5m3luaa-im58d

Find the general coefficient for a piecewise function:

https://wolfram.com/xid/0fq45s5m3luaa-eapwz3

General Fourier sine coefficient for a Gaussian function:

https://wolfram.com/xid/0fq45s5m3luaa-eag3i

Fourier sine coefficient for a basis function:

https://wolfram.com/xid/0fq45s5m3luaa-bc6x77


https://wolfram.com/xid/0fq45s5m3luaa-cqv1x

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.
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.
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
Wolfram Language. (2008). FourierSinCoefficient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FourierSinCoefficient.html
BibTeX
@misc{reference.wolfram_2025_fouriersincoefficient, author="Wolfram Research", title="{FourierSinCoefficient}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierSinCoefficient.html}", note=[Accessed: 12-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_fouriersincoefficient, organization={Wolfram Research}, title={FourierSinCoefficient}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierSinCoefficient.html}, note=[Accessed: 12-May-2025
]}