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 2 Integrate[expr Cos[2π b n t],{t,-,}] for n>0 and Integrate[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.