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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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