Function Repository Resource:

# NFourierSeries

Find a numerical approximation for an exponential Fourier series expansion of a function

Contributed by: Wolfram Research
 ResourceFunction["NFourierSeries"][expr,t,n] gives a numerical approximation to the nth-order Fourier series expansion of expr in t.

## Details and Options

The numerical approximation to the order n Fourier exponential series expansion of expr is by default defined to be , where Fk is given by .
With the setting FourierParameters{a,b}, the order n Fourier exponential series expansion computed by ResourceFunction["NFourierSeries"] is , where Fk is given by .
In addition to the option FourierParameters, ResourceFunction["NFourierSeries"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

## Examples

### Basic Examples

Numerical approximation for an exponential Fourier series:

 In[1]:=
 Out[1]=
 In[2]:=
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Compare with a plot of the original function:

 In[3]:=
 Out[3]=

## Requirements

Wolfram Language 11.3 (March 2018) or above