Re: numerical integration

• To: mathgroup at smc.vnet.net
• Subject: [mg69338] Re: numerical integration
• From: dimmechan at yahoo.com
• Date: Thu, 7 Sep 2006 23:58:05 -0400 (EDT)
• References: <edm1d1\$coc\$1@smc.vnet.net>

```So simple! Thanks.

The curious thing is that if you multiply with (exact) 1 you get

NIntegrate[1*BesselJ[0,x],{x,0,Infinity},Method->Oscillatory]
NIntegrate::oscfm: With Method->Oscillatory, the integrand should be a
product of an oscillatory function w[x] and another function f[x] , as
NIntegrate[ w[x] f[x],{x,a,Infinity}, Method->Oscillatory]. The
function w should be Sin, Cos, BesselJ, or BesselY, and f[x] should be
of the form a + b x^n for constant a and b. More...
NIntegrate[1 BesselJ[0,x],{x,0,Â¥},MethodÂ®Oscillatory]

while for e.g.

NIntegrate[3*BesselJ[0,x],{x,0,Infinity},Method->Oscillatory]
3.

Any suggestions?

Î?/Î? dimmechan at yahoo.com Î­Î³Ï?Î±Ï?Îµ:
> 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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