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Integral no longer evaluated in Version 7, 8

• To: mathgroup at smc.vnet.net
• Subject: [mg114410] Integral no longer evaluated in Version 7, 8
• From: John Jowett <john.m.jowett at gmail.com>
• Date: Fri, 3 Dec 2010 05:22:51 -0500 (EST)

Hello,
        With Mathematica Version 7, the integral

Integrate[(x^2/2)*BesselK[5/3, x], {x, 0, Infinity}]

correctly evaluated to (8*Pi)/(9*Sqrt[3]).  In Mathematica 7 or 8, it
gives the message

Integrate::idiv: Integral of x^2 BesselK[5/3,x] does not converge on
{0,\[Infinity]}. >>

I haven't been able to find any way to get this to work (NIntegrate
works fine). Termwise integration of the asymptotic form of the
integrand works but does not appear to converge.

Can anybody explain why Mathematica lost this capability?  It may have
something to do with no longer recognising cancellations among
expressions involving the Gamma function.  Any ideas for getting the
integral to work ?

Thanks,
John Jowett