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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.
  • The n^(th)-order Fourier sine series of f(t) is by default defined to be sum_(k=1)^nb_k sin(k t) with .
  • The m-dimensional Fourier sine series of f(t_1,t_2,...) is given by sum_(k_1=0)^(n_1)sum_(k_2=0)^(n_2)... b_(k_1,k_2,... )sin(k_1 t_1)sin(k_2 t_2)... 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}sum_(k=1)^nb_k sin(k t)
{1, 2Pi}sum_(k=1)^nb_k sin(2 pi k t)
{a, b}
  • The Fourier sine series of f(t) is equivalent to the Fourier series of .
EXAMPLESCLOSE ALL
Basic Examples   (2)
Find the 5^(th)-order Fourier sine series approximation to t:
Find the 3^(rd)-order bivariate Fourier sine series approximation to x y:
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 x y:
In[1]:=
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Out[1]=
In[2]:=
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Out[2]=
Scope   (3)
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:
Options   (1)
Use a non-default setting for FourierParameters:
Properties & Relations   (2)
The Fourier sine series of t^2:
The Fourier series of the odd extension of t^2:
In general these will always coincide:
The Fourier sine series of t^2 approximates :
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