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