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 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 .

Examples

open allclose all

Basic Examples  (2)

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

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

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

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Scope  (3)

Options  (1)

Properties & Relations  (1)

See Also

FourierSinCoefficient  FourierDST  FourierTrigSeries  FourierCosSeries  FourierSeries  Fourier  Integrate

Introduced in 2008
(7.0)