FourierSinTransform
- To: mathgroup at smc.vnet.net
- Subject: [mg70288] FourierSinTransform
- From: dimmechan at yahoo.com
- Date: Wed, 11 Oct 2006 01:54:25 -0400 (EDT)
Consider the following function
h[j_] := Sqrt[1 + l^2*j^2]/j
Then (the integral exists in the Hadamard sense)
FourierSinTransform[h[j], j, x]
-(MeijerG[{{1}, {}}, {{-(1/2), 1/2}, {0}}, x^2/(4*l^2)]/(2*Sqrt[2*Pi]))
Also
FullSimplify[FourierSinTransform[%, x, j], {l > 0, j > 0}]
Sqrt[l^2 + 1/j^2]
Can I trust the first result?
Thanks in adance for any response.