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Mathematica > Mathematics and Algorithms > Calculus > Integral Transforms >

Built-in Mathematica Symbol

FourierCosTransform

]
gives the symbolic Fourier cosine transform of expr.

FourierCosTransform[expr, {t₁, t₂, ...}, {

₁,

₂, ...}]
gives the multidimensional Fourier cosine transform of expr.

Different choices of definitions can be specified using the option FourierParameters.

With the setting the Fourier cosine transform computed by FourierCosTransform is .

Assumptions and other options to Integrate can also be given in FourierCosTransform.

Elementary functions:

Special functions:

Generalized functions:

Multivariate transform:

Fourier cosine transform of BesselJ is a piecewise function:

The default setting for FourierParameters is {0, 1}:

Use a non-default setting for a different definition of transform:

To get the inverse, use the same FourierParameters setting:

Use GenerateConditions->True to get parameter conditions for when a result is valid:

Results from FourierCosTransform and FourierTransform agree for even functions:

Fourier cosine transform may be given in terms of generalized functions such as DiracDelta: