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Function Repository Resource:

InverseFourierCoefficient

Source Notebook

Find a function with a given Fourier exponential series

Contributed by: Wolfram Research

ResourceFunction["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

The Fourier exponential series representation used by ResourceFunction["InverseFourierCoefficient"] is by default defined to be .
ResourceFunction["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 ResourceFunction["InverseFourierCoefficient"] is , a periodic function of t with period .

Examples

Basic Examples

Find a function with a given Fourier series:

In[1]:=
ResourceFunction["InverseFourierCoefficient"][1/(3 n + 1)^2, n, t]
Out[1]=

Compare with the answer from a numerical approximation:

In[2]:=
ResourceFunction["InverseFourierCoefficient"][1/(3 n + 1)^2, n, t]
Out[2]=
In[3]:=
% /. {t -> 0.6}
Out[3]=
In[4]:=
ResourceFunction["NInverseFourierCoefficient"][1/(3 n + 1)^2, n, 0.6]
Out[4]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

License Information