Re: Frustration with opaque functions in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg93270] Re: Frustration with opaque functions in Mathematica*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 1 Nov 2008 05:13:39 -0500 (EST)*References*: <geeedj$agl$1@smc.vnet.net>

Hi, http://mathworld.wolfram.com/MeijerG-Function.html http://functions.wolfram.com/HypergeometricFunctions/MeijerG/ http://functions.wolfram.com/HypergeometricFunctions/MeijerG1/ ?? Regards Jens Aaron Fude wrote: > Hi, > > This is a followup to a previous message, but I find that answers in > terms of MeijerG and Hypergeometric* have limited utility. > > For example, even mathematica cannot simplify them satisfactorily. I > find myself needing an answer in terms of elementary (or nearly > elementary) functions and I find that MeijerG is largely useless. I > understand that I can evaluate them, decompose in series, find limits, > graph, etc., but what I need is analytical insight which they do not > provide. > > eqn = r^2 y''[r] + r y'[r] + (r^2) y[r] == r BesselJ[1, r]; > soln = y[r] /. Assuming[Element[m, Integers] && m > 0, DSolve[eqn, > y[r], r][[1]]] // FullSimplify > r^2 D[soln, {r, 2}] + r D[soln, r] + r^2 soln - r BesselJ[1, r] // > FullSimplify > > So how can I find out what MeijerG[{{1, 1}, {1/2}}, {{1, 1}, {0, 0, > 0}}, r, 1/2] really is? > > Many thanks in advance, > > Aaron >