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FourierTrigSeries

As of Version 7.0, FourierTrigSeries is part of the built-in Mathematica kernel.

FourierTrigSeries[expr, t, k]
gives the order n Fourier trigonometric series expansion of expr, where expr is a periodic function of t with period 1.

MORE INFORMATION

To use FourierTrigSeries, you first need to load the Fourier Series Package using Needs["FourierSeries`"].

The order n Fourier exponential series expansion of expr is by default defined to be .

The coefficient c_k is defined to be and the coefficient d_k is defined to be .

Different choices for the period of expr can be specified using the option FourierParameters.

With the setting FourierParameters->{a, b}, expr is assumed to have a period of , and the order n Fourier exponential series expansion computed by FourierTrigSeries is . Here, the coefficient c_k is defined to be and the coefficient d_k is defined to be .

In addition to the option FourierParameters, FourierTrigSeries can also accept the options available to Integrate. These options are passed directly to Integrate.

Basic Examples (1)

Needs["FourierSeries`"]

Compute the trigonometric Fourier series for a periodic function of t with period 1:

Compare with a plot of the original function:

Fourier Series Package

Fourier Series Package

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