OBSOLETE FOURIER SERIES PACKAGE SYMBOL

# FourierCoefficient

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

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

## Details and OptionsDetails and Options

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

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

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

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Compare with the answer from a numerical approximation:

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