NFourierSinCoefficient


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

DetailsDetails

  • To use , you first need to load the Fourier Series Package using Needs["FourierSeries`"].
  • The numerical approximation to the n^(th) coefficient in the Fourier sine series expansion of expr is by default defined to be NIntegrate[expr Sin[n t], {t, 0, }], where n must be an integer.
  • Different choices for the definition of the Fourier sine 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 NIntegrate[expr Sin[b n t], {t, 0, }].
  • The parameter b in the setting FourierParameters->{a, b} must be numeric.
  • In addition to the option FourierParameters, can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

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Use different definitions for calculating numerical approximation for a Fourier sine coefficient:

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Compare with the answer from symbolic evaluation:

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