FourierSeries`
FourierSeries`

# FourierCosCoefficient

As of Version 7.0, FourierCosCoefficient is part of the built-in Wolfram Language 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.

# Details and Options

• 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 2Integrate[expr Cos[2π n t],{t,-,}] for n>0 and Integrate[expr,{t,-,}] for n==0.
• 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 2b Integrate[expr Cos[2π b n t],{t,-,}] for n>0 and bIntegrate[expr,{t,-,}] for n==0.
• In addition to the option FourierParameters, FourierCosCoefficient can also accept the options available to Integrate. These options are passed directly to Integrate.

# Examples

## Basic Examples(1)

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

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Compare with the answer from a numerical approximation:

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