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FourierSinCoefficient

FourierSinCoefficient
gives the n^(th) coefficient in the Fourier sine series expansion of expr.
FourierSinCoefficient
gives a multidimensional Fourier sine coefficient.
  • The ^(th) coefficient in the Fourier sine series expansion of is by default given by .
  • The -dimensional Fourier sine coefficient is given by .
  • 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.
{1,1}default settings
{1,2Pi}period 1
{a,b}general setting
Find the 3^(rd) Fourier sine series coefficient:
Find the general term coefficient:
Plot the coefficient sequence:
Find the Fourier sine coefficient:
The general term:
Plot the coefficient sequence:
Find the 3^(rd) Fourier sine series coefficient:
In[1]:=
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Out[1]=
Find the general term coefficient:
In[2]:=
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Out[2]=
Plot the coefficient sequence:
In[3]:=
Click for copyable input
Out[3]=
 
Find the Fourier sine coefficient:
In[1]:=
Click for copyable input
Out[1]=
The general term:
In[2]:=
Click for copyable input
Out[2]=
Plot the coefficient sequence:
In[3]:=
Click for copyable input
Out[3]=
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:
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