FourierCosCoefficient

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


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 OptionsDetails and Options

  • To use , 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[2 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 is 2b Integrate[expr Cos[2 b n t], {t, -, }] for n>0 and bIntegrate[expr, {t, -, }] for n==0.
  • In addition to the option FourierParameters, can also accept the options available to Integrate. These options are passed directly to Integrate.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

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

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Compare with the answer from a numerical approximation:

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