Integrate[ x^2 * Erfc[a x] *(BesselJ[1, b x])^2 , {x, 0, Inf}]
- To: mathgroup at smc.vnet.net
- Subject: [mg100842] Integrate[ x^2 * Erfc[a x] *(BesselJ[1, b x])^2 , {x, 0, Inf}]
- From: "ralf.schaa" <ralf.schaa at gmail.com>
- Date: Tue, 16 Jun 2009 21:49:41 -0400 (EDT)
Hi group,
The integral
Integrate[ x^2 * Erfc[a x] *(BesselJ[1, b x])^2 , {x, 0, Inf}]
has a solution in Mathematica (in terms of HypergeometricPFQ)
My question: how did Mathematica know?
I tried the usual suspects:
i) for example Gradshteyn and Ryzhik (1965), p.769, 6.784 is very
close, but not close enough
ii) Abramowitz & Stegun hasn't got it on the menu either
Then how about expressing Erfc[a*x] in terms of...
Erfc(z)=-1/(sqrt(pi)) * IncompleteGamma[1/2,x^2]+1 (Grads.+Ryzh. p.
942)
...and hoping to get lucky? ... no alas!
sorry, this is a cross-post (also in sci.math.symbolic)...
Help!
-Ralf
- Follow-Ups:
- Re: Integrate[ x^2 * Erfc[a x] *(BesselJ[1, b x])^2 ,
- From: Daniel Lichtblau <danl@wolfram.com>
- Re: Integrate[ x^2 * Erfc[a x] *(BesselJ[1, b x])^2 ,