a difficult Bessel intergral
- To: mathgroup at smc.vnet.net
- Subject: [mg32479] a difficult Bessel intergral
- From: Roberto Brambilla <rlbrambilla at cesi.it>
- Date: Wed, 23 Jan 2002 00:59:53 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hi to all MG friend!
Solving an integral equation in polar coordinates I need
the following integral (that Mathematica4.1 cannot symb. solve)
L[x_,y_,s_] := Integrate[ p(p^2+s^2)^(-1/2) BesselJ[0, x p] BesselJ[0, y p],
where x,y s are real numbers >=0. Special cases:
L[0,y_,s_] := Exp[-y s]/y
L[x_,0,s_] := Exp[-x s]/x
L[x_,y_,0] := (z=Min[x,y];Z=Max[x,y]; (2/Pi) EllipticK[(z/Z)^2]/Z )
It looks like a common and innocent integral but tables I have (Abramowitz,
don't consider it. I'd like to know if it is present in the more extensive
(like Erdély, Prudnikov, Luke...) that I can't access.
Also the numerical computation gives a lot of troubles and is very slow
since the integrand is oscillatory. The option Method->(some method) does not
improve the evaluation. May be some anlytical prework has to be done before
Any suggestion will be gratefully accepteed.
Via Rubattino 54
rlbrambilla at cesi.it
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