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MathGroup Archive 2000

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Mod Bessel function bug ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22988] Mod Bessel function bug ?
  • From: "J.R. Chaffer" <jrchaff at nwlink.com>
  • Date: Sun, 9 Apr 2000 01:45:52 -0400 (EDT)
  • Organization: Northwest Link
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

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?

Thanks,

J.R. Chaffer



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