BUILT-IN MATHEMATICA SYMBOL

# FourierSinCoefficient

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

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

## Details and OptionsDetails and Options

• The coefficient in the Fourier sine series expansion of is by default given by .
• The -dimensional Fourier sine coefficient is given by .
• In the form FourierSinCoefficient[expr, t, n], n can be symbolic or a positive 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} default settings {1,2Pi} period 1 {a,b} general setting

## ExamplesExamplesopen allclose all

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

Find the 3 Fourier sine series coefficient:

 Out[1]=

Find the general term coefficient:

 Out[2]=

Plot the coefficient sequence:

 Out[3]=

Find the Fourier sine coefficient:

 Out[1]=

The general term:

 Out[2]=

Plot the coefficient sequence:

 Out[3]=