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MathGroup Archive 1999

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Re: Hypergeometric2F1[a,b,c,1] in v4

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18925] Re: Hypergeometric2F1[a,b,c,1] in v4
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 27 Jul 1999 22:17:26 -0400
  • Organization: Universitaet Leipzig
  • References: <7ni7tv$5s4@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

you mean Abramowitz Stegun eqn 15.1.20

a) the replacement of Mathematica 3.0 is only right for 
   NotEqual[c,{0,-1,-2,-3,..}] and Re[c-a-b]>0
b) you can simply force the replacment with
   hprule = Hypergeometric2F1[a_, b_, c_, 1] :> 
              Gamma[c]*Gamma[c - a - b]/(Gamma[c - a]*Gamma[c - b])

   and
 
    yourExpression /. hprule

The correct form of the rule whould be

   hprule = Hypergeometric2F1[a_, b_, c_, 1] /;
                  Not[Element[c, Integers]] && c <= 0 && Re[c - a - b] >
0 :> 
              Gamma[c]*Gamma[c - a - b]/(Gamma[c - a]*Gamma[c - b])

but Mathematica can't make a decision of symbolic arguments and for
numeric 
arguments Mathematica calculate the function value any way.

Hope that helps
Jens

"C. Burger" wrote:
> 
> Mathematica v3 simplified Hypergeometric2F1[a,b,c,1] to the well-known
> expression involving Gamma functions.
> 
> Mathematica v4 does no longer do this. Did this functionality move to
> some external package which is not loaded by default? Am I missing
> something? Any assumptions on the parameters maybe?
> 
> --
> C. Burger
> MPI Colloids & Interfaces, D-14424 Potsdam-Golm, Germany
> burger at mpikg-golm.mpg.de


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