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FourierSinTransform
*To*: mathgroup at smc.vnet.net
*Subject*: [mg70283] FourierSinTransform
*From*: dimmechan at yahoo.com
*Date*: Wed, 11 Oct 2006 01:53:59 -0400 (EDT)
Consider the following function
h[Î¾_] := Sqrt[1 + l^2*Î¾^2]/Î¾
Then (the integral exists in the Hadamard sense)
FourierSinTransform[h[Î¾], Î¾, x]
-(MeijerG[{{1}, {}}, {{-(1/2), 1/2}, {0}}, x^2/(4*l^2)]/(2*Sqrt[2*Pi]))
Also
FullSimplify[FourierSinTransform[%, x, Î¾], {l > 0, Î¾ > 0}]
Sqrt[1 + l^2*Î¾^2]/Î¾
Can I trust the first result?
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