# FourierCosTransform

FourierCosTransform[expr,t,ω]

gives the symbolic Fourier cosine transform of expr.

FourierCosTransform[expr,{t1,t2,},{ω1,ω2,}]

gives the multidimensional Fourier cosine transform of expr.

# Details and Options

• The Fourier cosine transform of a function is by default defined to be .
• The multidimensional Fourier cosine transform of a function is by default defined to be .
• Other definitions are used in some scientific and technical fields.
• 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.

# Examples

open allclose all

## Scope(5)

Elementary functions:

Special functions:

Generalized functions:

Periodic functions:

Multivariate transform:

## Options(3)

### Assumptions(1)

Fourier cosine transform of BesselJ is a piecewise function:

### FourierParameters(1)

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

Use a nondefault setting for a different definition of transform:

To get the inverse, use the same FourierParameters setting:

### GenerateConditions(1)

Use to get parameter conditions for when a result is valid:

## Properties & Relations(3)

Use Asymptotic to compute an asymptotic approximation:

FourierCosTransform and InverseFourierCosTransform are mutual inverses:

Results from FourierCosTransform and FourierTransform agree for even functions:

The results agree for ω>0:

## Possible Issues(1)

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

## Neat Examples(1)

Wolfram Research (1999), FourierCosTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierCosTransform.html.

#### Text

Wolfram Research (1999), FourierCosTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/FourierCosTransform.html.

#### CMS

Wolfram Language. 1999. "FourierCosTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FourierCosTransform.html.

#### APA

Wolfram Language. (1999). FourierCosTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FourierCosTransform.html

#### BibTeX

@misc{reference.wolfram_2022_fouriercostransform, author="Wolfram Research", title="{FourierCosTransform}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/FourierCosTransform.html}", note=[Accessed: 23-March-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_fouriercostransform, organization={Wolfram Research}, title={FourierCosTransform}, year={1999}, url={https://reference.wolfram.com/language/ref/FourierCosTransform.html}, note=[Accessed: 23-March-2023 ]}