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: