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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 .
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