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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122856] Re: large integration result for simple problem: 1/x,, also BesselJ
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 12 Nov 2011 07:36:11 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201111110955.EAA08514@smc.vnet.net>

Mathematica 8 gives:

Integrate[BesselJ[n, b*x], {x, 0, Infinity},  Assumptions -> {Re[n] > -1, Im[b] == 0}]

Sign[b]^n/Abs[b]



Note the additional assumption on b. Without it the result is clearly not true.

Andrzej Kozlowski


On 11 Nov 2011, at 10:55, Richard Fateman wrote:

> (at least in Mathematica 7.0)
>
> try
>
> Integrate[1/x,{x,a,b}]
>
> Also
>
> Integrate[BesselJ[n, b*x], {x, 0, Infinity},   Assumptions -> Re[n] > -1 ]
>
> which returns an expression including this ....
>
> b^(-2 + n) (b^2)^(1/2 - n/2)
>
> which should be possible to simplify.  For example, for b>0, the
> expression is 1/b.
>
> maybe  1/b * If[b>0, 1 ,  -(-1)^n]  or so.
>
> I've been playing with integration of expressions involving Bessel
> functions.  Mathematica is sometimes surprising, on both sides of the
> ledger -- (Yes we Can and No we Can't).
>
>
> RJF
>
>




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