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FourierSinTransform


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?


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