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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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