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>