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MathGroup Archive 2002

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Re: Problem with hypergeometric function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34815] Re: [mg34796] Problem with hypergeometric function
  • From: BobHanlon at aol.com
  • Date: Sat, 8 Jun 2002 05:21:26 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 6/7/02 1:15:00 AM, ignacio at sgirmn.pluri.ucm.es writes:

>$Version
>
>Microsoft Windows 3.0 (April 25, 1997)
>
>Hi all,
>I have noticed some problems when trying to evaluate numerically certain
>
>hypergeometric functions.
>For example:
>
>f=HypergeometricPFQ[{1/2},{1,3/2},-8000]
>
>N[f]
>
>-1.34969 x 10^57
>
>a bit big, isn't it?
>
>$MaxExtraPrecision=200
>N[N[f,30]]
>
>0.00586605
>
>This seems more reasonable. The reason for this odd behaviour is related
>
>to how this expressions are evaluated. Essencially, N applies itself to
>
>any subexpression of f, as if MapAll were used.
>So, in the first case, HypergeometricPFQ finds machine precission 
>numbers as its arguments, and evaluates itself in the same way. The 
>algorithm is obviously not very fortunate (a series expansion, I 
>guess?), and so is not the result. In the second case, their arguments
>
>are arbitrary precision numbers, and even though the same problems are
>
>present, using extremely high precision numbers for the intermediate 
>calculation does the trick.
>
>My version of Mathematica is a bit old, and I would like to know if this
>
>problem remains in newer versions.
>
>I would also like to recommend to Mathematica developers to switch to 
>arbitrary precision arithmetic in all those cases in which they do not
>
>know for sure if the algorithm that is being used will give reliable 
>results in case of using machine size arithmetic.
>

$Version

4.1 for Mac OS X (November 5, 2001)

f=HypergeometricPFQ[{1/2},{1,3/2},-8000];

N[f]

0.00586605


Bob Hanlon
Chantilly, VA  USA


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