This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FourierSinCoefficient

 FourierSinCoefficient gives the n coefficient in the Fourier sine series expansion of expr. FourierSinCoefficientgives a multidimensional Fourier sine coefficient.
• The 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 \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define Fourier series GenerateConditions False whether 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 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 Fourier sine series coefficient:
 Out[1]=
Find the general term coefficient:
 Out[2]=
Plot the coefficient sequence:
 Out[3]=

Find the Fourier sine coefficient:
 Out[1]=
The general term:
 Out[2]=
Plot the coefficient sequence:
 Out[3]=
 Scope   (4)
Find the 5 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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