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Hankel transform question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82404] Hankel transform question
  • From: Jim Rockford <jim.rockford1 at gmail.com>
  • Date: Fri, 19 Oct 2007 05:04:31 -0400 (EDT)

I'm getting some disparate (or at least different looking) results for
a particular Hankel transform related integral in Mathematica 5.2
versus Mathematica 6.01.

The integral I'm dealing with is the order-V Hankel transform of a
constant ( f(r) = 1, say )

Define
g[s_] = s BesselJ[V,w s]

and I need  the output for

Integrate[g[s],{s,0,Infinity}]

Both versions of Mathematica complain about not being able to verify
convergence.  I believe this integral should give back a Dirac delta
function.  Here are the outputs:

*****************
   version 5.2
*****************
V/w^2      ( with V and w real and positive)

*****************
  version 6.01
*****************
Integrate::idiv:  Integral of s BesselJ[V,w s] does not converge on
(0,Infinity) >>


(1) First of all, what accounts for the differences in output between
the two versions of Mathematica?
(2) Second, I know that   Integrate[s BesselJ[0,s],{s,0,Infinity}]
should give Delta(s), but Mathematica 5.2  gives back the answer 0,
and Mathematica 6.01 again balks and says that the integral doesn't
converge.

Is there any way for me to get Mathematica to "look for" Delta
functions, instead of trying to grind out a numerical integration?

Thanks,
Jim



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