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Mathematica > Mathematics and Algorithms > Calculus > Integral Transforms > Fourier Analysis > FourierSinCoefficient >

BUILT-IN MATHEMATICA SYMBOL

FourierSinCoefficient

gives the n

coefficient in the Fourier sine series expansion of expr.

gives a multidimensional Fourier sine coefficient.

MORE INFORMATION

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, 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

Fourier sine coefficient:

The general term:

Plot the coefficient sequence:

Find the 3

Fourier sine series coefficient:

In[1]:=

Out[1]=

Find the general term coefficient:

In[2]:=

Out[2]=

Plot the coefficient sequence:

In[3]:=

Out[3]=

Find the

Fourier sine coefficient:

In[1]:=

Out[1]=

The general term:

In[2]:=

Out[2]=

Plot the coefficient sequence:

In[3]:=

Out[3]=

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: