Re: Mod Bessel function bug ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg23014] Re: [mg22988] Mod Bessel function bug ?*From*: "J.R. Chaffer" <jrchaff at nwlink.com>*Date*: Tue, 11 Apr 2000 23:18:32 -0400 (EDT)*References*: <88.2313422.26229972@aol.com>*Sender*: owner-wri-mathgroup at wolfram.com

Well, something is very strange. Thank both of you for your replies. I am using Mathematica Student Version 4.0; supposedly same as full version capabilities, or at least so advertised. My plots show there is a difference near zero; however, both functions come together (and become large) for large argument, precisely opposite to what bessel theory says. Supposedly, the I function with negative, noninteger order is the same as the K function (not with Mathematica), and the K function goes to zero exponentially with large argument. Something is definitely wrong. jrc BobHanlon at aol.com wrote: > DSolve[y''[x] - b^4*x^2*y[x] == 0, y[x], x] > > {{y[x] -> Sqrt[x]*BesselI[-(1/4), (b^2*x^2)/2]*C[1] + > Sqrt[x]*BesselI[1/4, (b^2*x^2)/2]*C[2]}} > > These two Bessel functions are different as shown by their plots > > b = 10; xmax = 2/b; > > Plot[{x^(1/2)*BesselI[-1/4, (b^2*x^2)/2], > x^(1/2)*BesselI[1/4, (b^2*x^2)/2]} , {x, 0, xmax}, > PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}, PlotRange -> All]; > > Bob Hanlon > > In a message dated 4/9/2000 2:02:32 AM, jrchaff at nwlink.com writes: > > >I am trying to solve the differential equation, > > > >y''[x] - b^4*x^2*y[x]=0; > > > >Mathematica gives two indep solutions: > > > >y = c1*x^1/2*BesselI{-1/4,b^2*x^2/2} > > + c2*x^1/2*BesselI{1/4,b^2*x^2/2}; > > > >Now, since the order is not an integer, one would > >think that the first term, with order -1/4, is the same > >as the Modified Bessel "K" function, (times root x) > >so would go to zero with large x. > > > >However, plotting each term individually shows that > >Mathematica considers these two terms identical (!). > >So how can it claim they are independent solutions? > > > >Or am I making some mistake? > >