Re: Hypergeometric rational/real discrepancy (bug?)
- To: mathgroup at smc.vnet.net
- Subject: [mg34142] Re: [mg34117] Hypergeometric rational/real discrepancy (bug?)
- From: BobHanlon at aol.com
- Date: Mon, 6 May 2002 05:20:11 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 5/4/02 5:50:18 AM, dreeves at eecs.umich.edu writes:
>Any reason why these 2 lines should produce such different results:
>
>Hypergeometric2F1Regularized[1, m - 2, m + 1, x] /. {m -> 1, x -> 1}
>
>Hypergeometric2F1Regularized[1, m - 2, m + 1, x] /. {m -> 1, x -> 1.}
>
>I'm using Mathematica 4.1 -- same result on Linux, Solaris, and Windows.
>
Same problem on a Mac OS X
$Version
4.1 for Mac OS X (November 5, 2001)
Hypergeometric2F1Regularized[1, m-2, m+1, x]/.
{{m->1, x->1}, {x->1, m->1},
{m->1, x->1.}, {x->1., m->1}}
{1/2, 1/2, 0.25, 0.25}
If this function is expanded before substitution the problem is avoided
FunctionExpand[
Hypergeometric2F1Regularized[1, m-2, m+1, x]]/.
{{m->1, x->1}, {x->1,
m->1},
{m->1, x->1.}, {x->1., m->1}}
{1/2, 1/2, 0.5, 0.5}
It also works properly if the substitutions are taken in two steps
with m substituted first
Hypergeometric2F1Regularized[1, m-2, m+1, x]/.
m->1 /. x->1.
0.5
Plot3D[Hypergeometric2F1Regularized[1, m-2, m+1, x],
{m, .5, 1.5}, {x, 0, 1},
PlotRange -> {Automatic, Automatic, {0.25,1}}];
Plot3D[Hypergeometric2F1[1, m-2, m+1, x]/
Gamma[m+1], {m, 0.5, 1.5}, {x, 0, 1},
PlotRange -> {Automatic, Automatic, {0.25,1}}];
Bob Hanlon
Chantilly, VA USA