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

BUILT-IN MATHEMATICA SYMBOL

FourierSinSeries

gives the n

-order Fourier sine series expansion of expr in t.

FourierSinSeries

gives the multidimensional Fourier sine series of expr.

MORE INFORMATION

The -order Fourier sine series of is by default defined to be with .

The -dimensional Fourier sine series of is given by with .

The following options can be given:

Assumptions	$Assumptions	assumptions on parameters
FourierParameters	{1,1}	parameters to define Fourier sine series
GenerateConditions	False	whether to generate results that involve conditions on parameters

Common settings for FourierParameters include:

	{1,1}
	{1,2Pi}
	{a,b}

The Fourier sine series of is equivalent to the Fourier series of .

EXAMPLES

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Basic Examples (2)

Find the 5

-order Fourier sine series approximation to t:

Find the 3

-order bivariate Fourier sine series approximation to

Find the 5

-order Fourier sine series approximation to t:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Find the 3

-order bivariate Fourier sine series approximation to

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (3)

Find the 3

-order Fourier sine series approximation to a quadratic polynomial:

Fourier sine series for a piecewise function:

The Fourier sine series for a basis function has only one term:

Options (1)

Use a nondefault setting for

FourierParameters:

Properties & Relations (1)

The Fourier sine series of

The Fourier series of the odd extension of

In general these will always coincide:

The Fourier sine series of

approximates