Frustration with opaque functions in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg93223] Frustration with opaque functions in Mathematica*From*: Aaron Fude <aaronfude at gmail.com>*Date*: Fri, 31 Oct 2008 03:08:34 -0500 (EST)

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