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MathGroup Archive 2006

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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.


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