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FourierCosCoefficient

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

FourierCosCoefficient[expr, t, n]
gives the n

coefficient in the Fourier cosine series expansion of expr, where expr is a periodic function of t with period 1.

MORE INFORMATION

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

The n coefficient in the Fourier cosine series expansion of expr is by default defined to be for n>0 and for n0.

If n is numeric, it should be an explicit integer.

Different choices for the definition of the Fourier cosine series expansion can be specified using the option FourierParameters.

With the setting FourierParameters->{a, b}, expr is assumed to have a period of , and the n coefficient computed by FourierCosCoefficient is for n>0 and for n0.

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

Basic Examples (1)

Needs["FourierSeries`"]

Use different definitions for calculating a coefficient in a Fourier cosine series:

Compare with the answer from a numerical approximation:

FourierCoefficient FourierSinCoefficient NFourierCoefficient NFourierSinCoefficient NFourierCosCoefficient InverseFourierCoefficient NInverseFourierCoefficient

Fourier Series Package

Fourier Series Package

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