# FourierSeries

FourierSeries[expr,t,n]

gives the n -order Fourier series expansion of expr in t.

FourierSeries[expr,{t1,t2,},{n1,n2,}]

gives the multidimensional Fourier series.

# Details and Options • The  -order Fourier series of is by default defined to be with .
• The multidimensional Fourier series of is given by with .
• The following options can be given:
•  Assumptions \$Assumptions assumptions on parameters FourierParameters {1,1} parameters to define Fourier series GenerateConditions False whether to generate results that involve conditions on parameters
• Common settings for FourierParameters include:
•  {1,1}  {1,–2Pi}  {a,b}  # Examples

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## Basic Examples(2)

Find the 3 -order Fourier series of :

Compute an order {2,2} Fourier series:

## Scope(4)

Find the 3 -order Fourier series of an exponential function:

Fourier series for a Gaussian function:

Fourier series for Abs:

Fourier series for a basis function has only one term:

## Options(1)

### FourierParameters(1)

Use a nondefault setting for FourierParameters:

Introduced in 2008
(7.0)