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Re: A question regarding a hyperbolic geometric function

• To: mathgroup at smc.vnet.net
• Subject: [mg86414] Re: A question regarding a hyperbolic geometric function
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Tue, 11 Mar 2008 02:55:24 -0500 (EST)
• References: <fr2mhu$o5p$1@smc.vnet.net>

"Ali K. Ozdagli" <ozdagli at gmail.com> wrote:
> Hi,
>
> I am working with Mathematica in order to solve an ordinary
> differential equation with several boundary conditions. It turned out
> that the solution is Kummer confluent hypergeometric function,
> HyperGeometric1F1[a,b,x]. My problem is that for the values of a, b
> and x I am interested in, e.g. a=-26.9, b=-20.1, x=300000, the
> numerical accuracy of Mathematica is very poor.
>
> Can somebody suggest me a way to improve the mathematical accuracy of
> HyperGeometric1F1? I prefer a quick and easy way but also appreciate
> any hard way.

I don't know if you're right or wrong. But as an example, let's use the
values you mentioned above for a, b and x. In version 6.0.2, I get

In[15]:= N[Hypergeometric1F1[-269/10, -201/10, 300000], 14]

Out[15]= 2.9932104092161 * 10^130260

Is that very poor numerical accuracy? If so, what should Out[15] have been?

David