InverseFourierCosTransform

InverseFourierCosTransform[expr,ω,t]

gives the symbolic inverse Fourier cosine transform of expr.

InverseFourierCosTransform[expr,{ω1,ω2,…},{t1,t2,…}]

gives the multidimensional inverse Fourier cosine transform of expr.

Details and Options

  • The inverse Fourier cosine transform of a function is by default defined as .
  • The multidimensional inverse Fourier cosine transform of a function is by default defined as .
  • Other definitions are used in some scientific and technical fields.
  • Different choices of definitions can be specified using the option FourierParameters.
  • With the setting FourierParameters->{a,b} the inverse Fourier transform computed by InverseFourierCosTransform is .
  • Assumptions and other options to Integrate can also be given in InverseFourierCosTransform.

Examples

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Basic Examples  (3)

Scope  (5)

Elementary functions:

Special functions:

Generalized functions:

Periodic functions:

Multivariate transforms:

Options  (3)

Assumptions  (1)

Use assumptions to indicate the region of interest for the parameters:

FourierParameters  (1)

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

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

GenerateConditions  (1)

Use GenerateConditions->True 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:

For even functions results are identical to InverseFourierTransform:

The results agree for ω>0:

Possible Issues  (1)

Inverse Fourier cosine transforms may require generalized functions such as DiracDelta:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_inversefouriercostransform, author="Wolfram Research", title="{InverseFourierCosTransform}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/InverseFourierCosTransform.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_inversefouriercostransform, organization={Wolfram Research}, title={InverseFourierCosTransform}, year={1999}, url={https://reference.wolfram.com/language/ref/InverseFourierCosTransform.html}, note=[Accessed: 22-December-2024 ]}