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MathGroup Archive 2007

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Re: a old post again

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72734] Re: [mg72715] a old post again
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Wed, 17 Jan 2007 06:24:38 -0500 (EST)
  • References: <200701160815.DAA29263@smc.vnet.net>

dimitris wrote:
> See again my post here
> 
> http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/b3548554d0d2089f/28be613fe6e90f20?lnk=gst&q=&rnum=1&hl=en#28be613fe6e90f20
> 
> I wonder why Mathematica 5.2 fails to evaluate symbolically the
> following integral
> 
> Integrate[(Log[a*x]/Sqrt[1 + x^2])*BesselJ[0, x], {x, 0, Infinity}]
> BesselI[0, 1/2]*BesselK[0, 1/2]*Log[a]
> 
> %/.a->0
> 0

Presumably you mean % /. a->1. In any case, the result of Integrate is 
wrong. The development version of Mathematica returns it unevaluated.


> NIntegrate[(Log[x]/Sqrt[1 + x^2])*BesselJ[0, x], {x, 0, Infinity},
> Method -> Oscillatory]
> -0.9979393746360525
> 
> whereas
> 
> Mathematica 4.0 succeds?
> 
> Regards
> Dimitris

"Succeeds" is a bit subjective. It returns an unevaluated Sum. A design 
decision was made to not allow such results. Actually I had thought this 
was decided long before version 4 so I'm surprised this persisted so 
long. There are now rare cases in which such sums may again be used as 
results for Integrate (piecewise integrands with infinitely many 
intervals of support).


Daniel Lichtblau
Wolfram Research





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