FourierCosCoefficient

FourierCosCoefficient[expr,t,n]

gives the n^(th) coefficient in the Fourier cosine series expansion of expr.

FourierCosCoefficient[expr,{t1,t2,},{n1,n2,}]

gives a multidimensional Fourier cosine coefficient.

Details and Options

  • The ^(th) coefficient in the Fourier cosine series expansion of is by default given by .
  • The dimensional Fourier cosine coefficient is given by .
  • In the form FourierCosCoefficient[expr,t,n], n can be symbolic or a nonnegative 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 5^(th) Fourier cosine coefficient:

Find the general term coefficient:

Plot the sequence:

Find the {3,5} Fourier cosine coefficient:

Find the coefficient of the general term:

Plot the multivariate sequence:

Scope  (4)

Find the 6^(th) Fourier cosine coefficient for a quadratic polynomial:

General Fourier cosine coefficient for a piecewise function:

Fourier cosine coefficient for a Gaussian function:

Fourier cosine coefficient for a basis function:

Options  (1)

FourierParameters  (1)

Use a nondefault setting for FourierParameters:

Introduced in 2008
 (7.0)