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FourierSeries

FourierSeries[expr, t, n]
gives the n^(th)-order Fourier series expansion of expr in t.
FourierSeries[expr, {t1, t2, ...}, {n1, n2, ...}]
gives the multidimensional Fourier series.
  • The n^(th)-order Fourier series of f(t) is by default defined to be sum_(k=-n)^nc_k ⅇ^(ⅈ k t) with .
  • The multidimensional Fourier series of f(t_1,t_2,...) is given by sum_(k_1=-n_1)^(n_1)sum_(k_2=-n_2)^(n_2)... c_(k_1,k_2,...) ⅇ^(ⅈ (k_1 t_1+k_2 t_2+...)) with .
  • 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
{1, 1}sum_(k=-n)^nc_k ⅇ^(ⅈ k t)
{1, -2Pi}sum_(k=-n)^nc_k ⅇ^(-ⅈ 2 pi k t)
{a, b}
EXAMPLESCLOSE ALL
Basic Examples   (2)
Find the 3^(rd) order Fourier series of t/2:
Compute an order {2,2} Fourier series:
Find the 3^(rd) order Fourier series of t/2:
In[1]:=
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Out[1]=
In[2]:=
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Out[2]=
 
Compute an order {2,2} Fourier series:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Scope   (4)
Find the 3^(rd) order Fourier series of an exponential function:
Fourier series for a Gaussian function:
Fourier series for Abs:
Fourier series for a basis function has only one term:
Options   (1)
Use a non-default setting for FourierParameters:
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