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?
> >