FourierSeries`
FourierSeries`

InverseFourierCoefficient

InverseFourierCoefficient[expr,n,t]

gives the function of t whose Fourier exponential series representation has coefficients given by expr, where expr is a function of n.

Details and Options

  • To use InverseFourierCoefficient, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
  • The Fourier exponential series representation used by InverseFourierCoefficient is by default defined to be expr -2πnt.
  • InverseFourierCoefficient returns a periodic function of t with default period 1.
  • 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 InverseFourierCoefficient is expr -2 πbnt, a periodic function of t with period .

Examples

Basic Examples  (1)

Find a function with a given Fourier series:

Compare with the answer from a numerical approximation: