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MathGroup Archive 2002

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Re: Problem with hypergeometric function

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

In a message dated 6/7/02 1:15:00 AM, ignacio at writes:

>Microsoft Windows 3.0 (April 25, 1997)
>Hi all,
>I have noticed some problems when trying to evaluate numerically certain
>hypergeometric functions.
>For example:
>-1.34969 x 10^57
>a bit big, isn't it?
>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.


4.1 for Mac OS X (November 5, 2001)




Bob Hanlon
Chantilly, VA  USA

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