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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


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