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

# FourierCoefficient

 FourierCoefficient gives the n coefficient in the Fourier series expansion of expr. FourierCoefficientgives a multidimensional Fourier coefficient.
• The coefficient in the Fourier series expansion of is by default given by .
• The -dimensional Fourier 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} f(t) e-i n tdt default settings {1,-2Pi} f(t) ei 2 n tdt period 1 {a,b} general setting
Find the 5 Fourier coefficient:
Find the coefficient of the general term in a Fourier series:
Plot the sequence:
Find the Fourier coefficient:
Find the coefficient of the general term:
Plot the absolute value of coefficients:
Find the 5 Fourier coefficient:
 Out[1]=
Find the coefficient of the general term in a Fourier series:
 Out[2]=
Plot the sequence:
 Out[3]=

Find the Fourier coefficient:
 Out[1]=
Find the coefficient of the general term:
 Out[2]=
Plot the absolute value of coefficients:
 Out[3]=
 Scope   (4)
Find the 3 Fourier coefficient for an exponential function:
General Fourier coefficient for a Gaussian function:
General Fourier coefficients for Abs:
Fourier coefficient for a basis exponential function:
 Options   (2)
Specify assumptions on a parameter:
Use a nondefault setting for FourierParameters:
FourierCoefficient is defined by an integral:
Compute the exponential Fourier series using the individual coefficients:
Fourier coefficients for basis exponentials:
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