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?
>