Re: Re: A question regarding a hyperbolic

• To: mathgroup at smc.vnet.net
• Subject: [mg86461] Re: [mg86423] Re: [mg86396] A question regarding a hyperbolic
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 12 Mar 2008 00:09:47 -0500 (EST)
• Reply-to: hanlonr at cox.net

```Negative accuracy is expected with large numbers since the digits immediately left of the decimal are not accurate. The result below has 13008 digits left of the decimal place. An accuracy of -12991.8 says that you cannot trust the 112992 digits immediately left of the decimal. Consequently, you should be able to trust the 16 most significant digits.

Bob Hanlon

---- "Ali K. Ozdagli" <ozdagli at gmail.com> wrote:
> Hi Bob and all,
>
> I originally figured this problem while I was working with a second
> order ODE of which solution involves Hypergeometric1F1. I have plugged
> the solution back to the ODE and it turned out that the equation is
> not satisfied for all values of the independent variable. I know the
> solution is correct as I have checked it both with Mathematica and
> another software. The mistake in the result becomes apparent when you
> check the accuracy and precision with Accuracy[] and Precision[]. For
> example, Hypergeometric1F1[-26.9, -20.1, 30000] gives
>
> 5.868090710725125*10^13007
>
> However, if you check accuracy and precision of the result you get
>
> Accuracy[Hypergeometric1F1[-26.9, -20.1, 30000]] = -12991.8 (negative is bad!!!)
> Precision[Hypergeometric1F1[-26.9, -20.1, 30000]] = 15.9546
>
> Where the latter is also the machine precision in Mathematica. This
> means that the results are precisely wrong although we want them to be
> roughly correct. :)
>
>
> Best,
>
> Ali
>
>
>
>
> On 3/10/08, Bob Hanlon <hanlonr at cox.net> wrote:
> > v1 = Hypergeometric1F1[-26.9, -20.1, 30000]
> >
> >  5.86809071072512533577549124209830605005026`\
> >   15.954589770191005*^13007
> >
> >  Use exact values until evaluating the Hypergeometric1F1 with extended precision
> >
> >  v2 = N[Hypergeometric1F1[-269/10, -201/10, 30000], 100]
> >
> >  5.86809071072500808515263985241332834422719\
> >   \
> >  6477241041525402740155487068020893691436344\
> >   \
> >  4849172908349727305685895816448516416585189\
> >   1451997662`100.*^13007
> >
> >  Although even without extra precision v1 is very close to v2
> >
> >  (v1 - v2)/v2
> >
> >  1.99810515261962031039159`2.2552081099371497\
> >   *^-14
> >
> >
> >
> >  Bob Hanlon
> >
> >
> >  ---- "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.
> >  >
> >  > Best,
> >  >
> >  > Ali
> >  >
> >  > --
> >  >
> >  > Ali K. Ozdagli
> >  > Ph.D. Student in Economics
> >  > at University of Chicago
> >  >
> >
> >
>
>
> --
>
> Ali K. Ozdagli
> Ph.D. Student in Economics
> at University of Chicago
>

```

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