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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 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 tdtdefault settings {1,-2Pi} 
f(t) ei 2
n tdtperiod 1 {a,b} 
general setting
Examplesopen all
Fourier coefficient: 
New in 7
