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