FourierSeries`
FourierSeries`

FourierCosCoefficient

As of Version 7.0, FourierCosCoefficient is part of the built-in Wolfram Language kernel.

FourierCosCoefficient[expr,t,n]

gives the n^(th) coefficient in the Fourier cosine series expansion of expr, where expr is a periodic function of t with period 1.

Details and Options

  • To use FourierCosCoefficient, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
  • The n^(th) coefficient in the Fourier cosine series expansion of expr is by default defined to be 2Integrate[expr Cos[2π n t],{t,-,}] for n>0 and Integrate[expr,{t,-,}] for n==0.
  • If n is numeric, it should be an explicit integer.
  • Different choices for the definition of the Fourier cosine series expansion can be specified using the option FourierParameters.
  • With the setting FourierParameters->{a,b}, expr is assumed to have a period of , and the n^(th) coefficient computed by FourierCosCoefficient is 2 Integrate[expr Cos[2π b n t],{t,-,}] for n>0 and Integrate[expr,{t,-,}] for n==0.
  • In addition to the option FourierParameters, FourierCosCoefficient can also accept the options available to Integrate. These options are passed directly to Integrate.

Examples

Basic Examples  (1)

Use different definitions for calculating a coefficient in a Fourier cosine series:

Compare with the answer from a numerical approximation:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_fouriercoscoefficient, author="Wolfram Research", title="{FourierCosCoefficient}", year="2008", howpublished="\url{https://reference.wolfram.com/language/FourierSeries/ref/FourierCosCoefficient.html}", note=[Accessed: 25-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_fouriercoscoefficient, organization={Wolfram Research}, title={FourierCosCoefficient}, year={2008}, url={https://reference.wolfram.com/language/FourierSeries/ref/FourierCosCoefficient.html}, note=[Accessed: 25-November-2024 ]}