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RE: A question regarding a hyperbolic geometric function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86431] RE: [mg86396] A question regarding a hyperbolic geometric function
  • From: "Tony Harker" <a.harker at ucl.ac.uk>
  • Date: Tue, 11 Mar 2008 02:58:38 -0500 (EST)

 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
]-> 
]-> 



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