FourierSinCoefficient

FourierSinCoefficient[expr,t,n]
gives the n^(th) coefficient in the Fourier sine series expansion of expr.

FourierSinCoefficient[expr,{t1,t2,},{n1,n2,}]
gives a multidimensional Fourier sine coefficient.

Details and OptionsDetails and Options

  • The ^(th) 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$Assumptionsassumptions on parameters
    FourierParameters{1,1}parameters to define Fourier series
    GenerateConditionsFalsewhether 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

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find the 3^(rd) Fourier sine series coefficient:

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Find the general term coefficient:

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Plot the coefficient sequence:

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Find the Fourier sine coefficient:

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The general term:

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Plot the coefficient sequence:

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Introduced in 2008
(7.0)