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FourierSinSeries

FourierSinSeries
gives the n^(th)-order Fourier sine series expansion of expr in t.
FourierSinSeries
gives the multidimensional Fourier sine series of expr.
  • 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
{1,1}
{1,2Pi}
{a,b}
  • The Fourier sine series of is equivalent to the Fourier series of .
Find the 5^(th)-order Fourier sine series approximation to t:
Find the 3^(rd)-order bivariate Fourier sine series approximation to :
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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Find the 3^(rd)-order Fourier sine series approximation to a quadratic polynomial:
Fourier sine series for a piecewise function:
The Fourier sine series for a basis function has only one term:
Use a nondefault setting for FourierParameters:
The Fourier sine series of :
The Fourier series of the odd extension of :
In general these will always coincide:
The Fourier sine series of approximates :
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