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Re: large integration result for simple problem: 1/x,, also BesselJ

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122861] Re: large integration result for simple problem: 1/x,, also BesselJ
  • From: Richard Fateman <fateman at eecs.berkeley.edu>
  • Date: Sat, 12 Nov 2011 07:37:05 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

On 11/11/2011 8:38 AM, Andrzej Kozlowski wrote:
> Mathematica 8 returns:
>
>
> Integrate[BesselJ[n, b*x], {x, 0, Infinity},
>   Assumptions ->  {Re[n]>  -1}]
>
>   b^(n - 2)*(b^2)^(1/2 - n/2)
>
> Andrzej Kozlowski

So by your previous note, this answer from version 8.0  is wrong since 
it does not exclude Im[b]==0.
I note that the formula is also wrong unless it somehow excludes b==0, 
when the integral is infinite,
but the formula is indeterminate.

Interestingly Gradshteyn & Rhyzik exclude all  b<=0 from their formula, 
with answer 1/b.

G&R probably figure that a human would know about the symmetries of 
Bessel functions, and would deal with a
negative coefficient in a sensible way. Just as an integral from 
-Infinity to 0 could be figured out, or some other integrals by a change 
of variables.


RJF



..snip..



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