       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][]] // 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?