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MathGroup Archive 2002

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Re: Problem with hypergeometric function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34809] Re: Problem with hypergeometric function
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 8 Jun 2002 05:21:16 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <adpfj2$j4c$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

yes Mathematica 4.1 gives

In[]:=N[f]
Out[]=0.00586605

Regards
  Jens

Ignacio Rodriguez wrote:
> 
> $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.


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