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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[ξ_] := Sqrt[1 + l^2*ξ^2]/ξ

Then (the integral exists in the Hadamard sense)

FourierSinTransform[h[ξ], ξ, x]
-(MeijerG[{{1}, {}}, {{-(1/2), 1/2}, {0}}, x^2/(4*l^2)]/(2*Sqrt[2*Pi]))

Also

FullSimplify[FourierSinTransform[%, x, ξ], {l > 0, ξ > 0}]
Sqrt[1 + l^2*ξ^2]/ξ

Can I trust the first result?