BUILT-IN WOLFRAM LANGUAGE 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 td t default settings {1,-2Pi} f(t) ei 2π n td t period 1 {a,b} general setting

## ExamplesExamplesopen allclose all

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

Find the 5 Fourier coefficient:

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

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Plot the sequence:

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Find the {3,5} Fourier coefficient:

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Find the coefficient of the general term:

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Plot the absolute value of coefficients:

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