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Re: A question regarding a hyperbolic geometric function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86437] Re: [mg86396] A question regarding a hyperbolic geometric function
  • From: "Ali K. Ozdagli" <ozdagli at gmail.com>
  • Date: Tue, 11 Mar 2008 02:59:45 -0500 (EST)
  • References: <200803100704.CAA24775@smc.vnet.net>

This would be a nice way to go. I have just checked the Abramowitz and
Stegun book but unfortunately there are no such transformations for
Hypergeometric1F1. Does anybody know a transformation for
Hypergeometric1F1 that can help me solve my numerical accuracy problem
the way Tony did below. Any other ideas are also appreciated.

Best,

Ali

On Mon, Mar 10, 2008 at 3:37 PM, Tony Harker <a.harker at ucl.ac.uk> wrote:
>
>   I suspect the problem might be the large value of the argument, which means
>  the series converges too slowly to be practicable. When I had a similar
>  problem a little while ago, with a different hypergeometric function, I
>  dragged my trusty Abramowitz and Stegun off the shelf and found a
>  transformation which solved the problem. In my case it was
>   Hypergeometric2F1[a_, b_, c_, z_] -> Gamma[c]Gamma[b -
>  a](-z)^(-a)Hypergeometric2F1[a, 1 - c + a,
>           1 - b + a, 1/z]/(Gamma[b] Gamma[c - a])
>
>  that did the trick -- there may be something similar for your problem.
>
>    Tony Harker
>
>  Dr A.H. Harker
>  Department of Physics and Astronomy
>  University College London
>  Gower Street
>  London
>  WC1E 6BT
>
>  Tel: (44)(0) 2076793404
>  E:    a.harker at ucl.ac.uk
>
>  ]-> -----Original Message-----
>  ]-> From: Ali K. Ozdagli [mailto:ozdagli at gmail.com]
>  ]-> Sent: 10 March 2008 07:05
>  ]-> To: mathgroup at smc.vnet.net
>  ]-> Subject: [mg86396] A question regarding a hyperbolic
>  ]-> geometric function
>  ]->
>  ]-> 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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