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?