       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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