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MathGroup Archive 2006

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numerical integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69309] numerical integration
  • From: dimmechan at yahoo.com
  • Date: Wed, 6 Sep 2006 04:28:30 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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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