FourierSinSeries

FourierSinSeries[expr,t,n]
gives the n^(th)-order Fourier sine series expansion of expr in t.

FourierSinSeries[expr,{t1,t2,},{n1,n2,}]
gives the multidimensional Fourier sine series of expr.

Details and OptionsDetails and Options

  • The ^(th)-order Fourier sine series of is by default defined to be with .
  • The -dimensional Fourier sine series of is given by with .
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    FourierParameters{1,1}parameters to define Fourier sine series
    GenerateConditionsFalsewhether to generate results that involve conditions on parameters
  • Common settings for FourierParameters include:
  • {1,1}
    {1,2Pi}
    {a,b}
  • The Fourier sine series of is equivalent to the Fourier series of .

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find the 5^(th)-order Fourier sine series approximation to t:

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Find the 3^(rd)-order bivariate Fourier sine series approximation to :

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Introduced in 2008
(7.0)