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Reproducing Hankel transform pairs?

Posted 5 years ago
POSTED BY: John Burkhardt

InverseHankelTransform[]'s support is still somewhat limited,so don't be surprised if some things don't work yet.

I have only workaround: InverseHankelTransform[ArcCos[rho], rho, r] is:

 InverseFourierCosTransform[
    InverseHankelTransform[FourierCosTransform[ArcCos[a rho], a, s], 
      rho, r, Assumptions -> {s > 0}][[1]], s, a] /. a -> 1 // Expand

(*(\[Pi] BesselJ[0, r/2] BesselJ[1, r/2])/(2 r) - (
I Sqrt[\[Pi]] MeijerG[{{}, {1/2}}, {{0, 1}, {0}}, r^2/4])/r^2*)

but solution is expressed by MeijerG function.

  FullSimplify[HankelTransform[%, r, rho] // FunctionExpand, 
   Assumptions -> 0 < rho < 1]
(*ArcCos[rho]*)
POSTED BY: Mariusz Iwaniuk
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