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.