InverseFourierSinTransform

InverseFourierSinTransform[expr,ω,t]

gives the symbolic inverse Fourier sine transform of expr.

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

gives the multidimensional inverse Fourier sine transform of expr.

Details and Options

  • The inverse Fourier sine transform of a function is by default defined as .
  • The multidimensional inverse Fourier sine 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 InverseFourierSinTransform is .
  • Assumptions and other options to Integrate can also be given in InverseFourierSinTransform.

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 the 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:

FourierSinTransform and InverseFourierSinTransform are mutual inverses:

For odd functions, results are identical to InverseFourierTransform except for a factor -I:

The results differ by a factor of -I for ω>0:

Possible Issues  (1)

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

Introduced in 1999
 (4.0)