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 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

Examples

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Basic Examples  (2)

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

Find the general term coefficient:

Plot the coefficient sequence:

Find the {3,5} Fourier sine coefficient:

The general term:

Plot the coefficient sequence:

Scope  (4)

Find the 5^(th) Fourier sine coefficient for a quadratic polynomial:

Find the general coefficient for a piecewise function:

General Fourier sine coefficient for a Gaussian function:

Fourier sine coefficient for a basis function:

Introduced in 2008
 (7.0)