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MathGroup Archive 2006

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Re: numerical integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69333] Re: numerical integration
  • From: p-valko at tamu.edu
  • Date: Thu, 7 Sep 2006 04:30:35 -0400 (EDT)
  • References: <edm1d1$coc$1@smc.vnet.net>

You just have to multiply the Bessel function by something. The
simplest is to put there 1.

NIntegrate[BesselJ[0, x] 1., {x, 0, Infinity}, Method -> Oscillatory]

The result will be:
1.





dimmechan at yahoo.com wrote:
> Hi.
>
> I posted a similar message before one month but since there was not a
> reply I repost just the basic questions again.
>
> 1) Why
>
> NIntegrate[BesselJ[0,x],{x,0,Infinity},Method->Oscillatory]
>
> does not work, while e.g.
>
> NIntegrate[BesselJ[0,x]BesselJ[1,x],{x,0,Infinity},Method->Oscillatory]
>
>
> works fine?
>
> 2) Why
>
> Integrate[BesselJ[n,x],{x,0,Infinity}]
>
> gives the following conditional result
>
> If[Re[n] > -1, 1, Integrate[BesselJ[n, x], {x, 0, Infinity},
> Assumptions -> Re[n] <= -1]]
>
> while
>
> Integrate[{BesselJ[ - 5,x],BesselJ[ - 8,x]},{x,0,Infinity}]
>
> Integrate::gener: Unable to check convergence. More...
>
> Integrate::gener: Unable to check convergence. More...
>
> {-1, -1}
>
> 3) Why exist the warning messages regarding convergence in the previous
> command as also
> in the following command?
>
> Integrate[BesselJ[0,x],{x,0,Infinity}]
>
> Integrate::gener: Unable to check convergence. More...
> 
> 1
> 
> Cheers,
> 
> Dimitrios Anagnostou


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