FourierSeries`

FourierSeries`

FourierSinCoefficient

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

FourierSinCoefficient[expr,t,n]

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

Details and Options

To use FourierSinCoefficient, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
The n coefficient in the Fourier sine series expansion of expr is by default defined to be 2Integrate[expr Sin[2π n t],{t,-,}].
If n is numeric, it should be an explicit integer.
Different choices for the definition of the Fourier sine 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 FourierSinCoefficient is 2 Integrate[expr Sin[2π b n t],{t,-,}].
In addition to the option FourierParameters, FourierSinCoefficient can also accept the options available to Integrate. These options are passed directly to Integrate.

Examples

Basic Examples (1)

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

Compare with the answer from a numerical approximation:

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