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

Built-in Mathematica Symbol

FourierCosCoefficient

FourierCosCoefficient[expr, t, n]
gives the n

coefficient in the Fourier cosine series expansion of expr.

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

MORE INFORMATION

The n coefficient in the Fourier cosine series expansion of is by default given by .

The -dimensional Fourier cosine coefficient is given by .

In the form FourierCosCoefficient[expr, t, n], n can be symbolic or a non-negative 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 5

Fourier cosine coefficient:

Find the general term coefficient:

Plot the sequence:

Find the

Fourier cosine coefficient:

Find the coefficient of the general term:

Plot the multivariate sequence:

Find the 5

Fourier cosine coefficient:

In[1]:=

Out[1]=

Find the general term coefficient:

Plot the sequence:

Find the

Fourier cosine coefficient:

In[1]:=

Out[1]=

Find the coefficient of the general term:

In[2]:=

Out[2]=

Plot the multivariate sequence:

In[3]:=

Out[3]=

Scope (4)

Find the 6

Fourier cosine coefficient for a quadratic polynomial:

General Fourier cosine coefficient for a piecewise function:

Fourier cosine coefficient for a Gaussian function:

Fourier cosine coefficient for a basis function:

Options (1)

Use a non-default setting for FourierParameters: