This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

FourierCosCoefficient

FourierCosCoefficient
gives the n^(th) coefficient in the Fourier cosine series expansion of expr.
FourierCosCoefficient
gives a multidimensional Fourier cosine coefficient.
  • The ^(th) coefficient in the Fourier cosine series expansion of is by default given by .
  • The -dimensional Fourier cosine 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 5^(th) Fourier cosine coefficient:
Find the general term coefficient:
Plot the sequence:
Find the Fourier cosine coefficient:
Find the coefficient of the general term:
Plot the multivariate sequence:
Find the 5^(th) Fourier cosine coefficient:
In[1]:=
Click for copyable input
Out[1]=
Find the general term coefficient:
In[2]:=
Click for copyable input
Out[2]=
Plot the sequence:
In[3]:=
Click for copyable input
Out[3]=
 
Find the Fourier cosine coefficient:
In[1]:=
Click for copyable input
Out[1]=
Find the coefficient of the general term:
In[2]:=
Click for copyable input
Out[2]=
Plot the multivariate sequence:
In[3]:=
Click for copyable input
Out[3]=
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:
Use a nondefault setting for FourierParameters:
New in 7