BUILT-IN MATHEMATICA SYMBOL

# FourierCoefficient

FourierCoefficient[expr, t, n]
gives the n coefficient in the Fourier series expansion of expr.

FourierCoefficient[expr, {t1, t2, ...}, {n1, n2, ...}]
gives a multidimensional Fourier coefficient.

## Details and OptionsDetails and Options

• The coefficient in the Fourier series expansion of is by default given by .
• The -dimensional Fourier coefficient is given by .
• In the form FourierCoefficient[expr, t, n], n can be symbolic or an integer.
• 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
• The function expr is assumed to be periodic in t with period , except when otherwise specified by FourierParameters.
• Common settings for FourierParameters include:
•  {1,1} f(t) e-i n tdt default settings {1,-2Pi} f(t) ei 2 n tdt period 1 {a,b} general setting

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Find the 5 Fourier coefficient:

 Out[1]=

Find the coefficient of the general term in a Fourier series:

 Out[2]=

Plot the sequence:

 Out[3]=

Find the Fourier coefficient:

 Out[1]=

Find the coefficient of the general term:

 Out[2]=

Plot the absolute value of coefficients:

 Out[3]=

### Properties & Relations (4)Properties & Relations (4)

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