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