FourierTrigSeries [expr,t,n]
gives the n^(th)-order Fourier trigonometric series expansion of expr in t.
FourierTrigSeries [expr,{t1,t2,…},{n1,n2,…}]
gives the multidimensional Fourier trigonometric series of expr.
FourierTrigSeries
FourierTrigSeries [expr,t,n]
gives the n^(th)-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^(th)-order Fourier trigonometric series of is by default defined to be with and .
- The following options can be given:
-
- With the setting FourierParameters->{a,b} the following series is returned: with and .
Examples
open all close allBasic Examples (2)
Find the 5^(th)-order Fourier trigonometric series of t:
Find the 3^(rd)-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 FourierParameters :
See Also
FourierSeries FourierSinSeries FourierCosSeries Fourier FourierTransform Integrate
Function Repository: NFourierTrigSeries TrigApproximateList
Related Guides
History
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_2025_fouriertrigseries, author="Wolfram Research", title="{FourierTrigSeries}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FourierTrigSeries.html}", note=[Accessed: 04-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_fouriertrigseries, organization={Wolfram Research}, title={FourierTrigSeries}, year={2008}, url={https://reference.wolfram.com/language/ref/FourierTrigSeries.html}, note=[Accessed: 04-December-2025]}