# 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 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

# Examples

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## Basic Examples(2)

Find the 3 Fourier sine series coefficient:

Find the general term coefficient:

Plot the coefficient sequence:

Find the {3,5} Fourier sine coefficient:

The general term:

Plot the coefficient sequence:

## Scope(4)

Find the 5 Fourier sine coefficient for a quadratic polynomial:

Find the general coefficient for a piecewise function:

General Fourier sine coefficient for a Gaussian function:

Fourier sine coefficient for a basis function: