InverseFourierCoefficient

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 ^-2πnt.
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 πbnt}, a periodic function of t with period .

Wolfram Language code: Needs["FourierSeries`"]

Find a function with a given Fourier series:

Wolfram Language code: InverseFourierCoefficient[1 / (3n + 1) ^ 2, n, t]

Compare with the answer from a numerical approximation:

Wolfram Language code: InverseFourierCoefficient[1 / (3n + 1) ^ 2, n, t]

Wolfram Language code: % /. {t -> 0.6}

Wolfram Language code: NInverseFourierCoefficient[1 / (3n + 1) ^ 2, n, 0.6]

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