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Re: Bug with Hypergeometric2F1?

• To: mathgroup at smc.vnet.net
• Subject: [mg99422] Re: [mg99384] Bug with Hypergeometric2F1?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Tue, 5 May 2009 05:43:41 -0400 (EDT)
• Reply-to: hanlonr at cox.net

It is a numerical precision problem

vol1[n_, k_] = Sum[Binomial[n, i], {i, 0, k}]

2^n - Binomial[n, k + 1]*Hypergeometric2F1[1, k - n + 1, k + 2, 
       -1]

vol1 @@@ {{1000, 1}, {1000, 1.}, {1000., 1}, {1000., 1.}}

{1001, 5.28426328596665*^288, 5.28426328596665*^288, 
   5.28426328596665*^288}

Increase the numerical precision of the input

vol1 @@@ {{1000, 1}, {1000, 1.`400},
   {1000.`400, 1}, {1000.`400, 1.`400}} // Round

{1001,1001,1001,1001}

Or change the function definition to force precision

vol1[n_, k_] := Sum[Binomial[Rationalize[n, 0], i],
  {i, 0, Rationalize[k, 0]}]

vol1 @@@ {{1000, 1}, {1000, 1.}, {1000., 1}, {1000., 1.}}

{1001,1001,1001,1001}


Bob Hanlon

---- irchans <infinitgames at yahoo.com> wrote: 

=============
When I run this code:

vol1[n_, k_] = Sum[ Binomial[n, i], {i, 0, k}]
vol1[1000, 1]
vol1[1000, 1.]

I get

Out[1] = 1001


Out[2] = 7.12935*10^288


I am running Mathematica 7.0.0 on windows 2000.  Does anyone else have
this problem?

• Follow-Ups:
  • Re: Re: Bug with Hypergeometric2F1?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>