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NInverseFourierCoefficient

 NInverseFourierCoefficient[expr, n, t]gives a numerical approximation to the function, evaluated at t, whose Fourier exponential series representation has coefficients given by expr, where expr is a function of n.
• The numerical approximation to the Fourier exponential series representation used by NInverseFourierCoefficient is by default defined to be NSum[expr -2 n t, {n, -, }].
• Different choices for the definition of the Fourier exponential series representation can be specified using the option FourierParameters.
• With the setting FourierParameters->{a, b}, the Fourier exponential series representation used by NInverseFourierCoefficient is .
• In addition to the option FourierParameters, NInverseFourierCoefficient can also accept the options available to NSum. These options are passed directly to NSum.
 例   (1)
Needs["FourierSeries`"]
Numerical approximation for a function with a given Fourier series:
 Out[2]=
Compare with the answer from symbolic evaluation:
 Out[3]=
 Out[4]=
 Out[5]=