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