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