Re: Limit of Hypergeometric2F1

*To*: mathgroup at smc.vnet.net*Subject*: [mg112657] Re: Limit of Hypergeometric2F1*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Sat, 25 Sep 2010 02:19:31 -0400 (EDT)*References*: <i7f3us$e37$1@smc.vnet.net>

On 23 sep, 10:43, Valeri Astanoff <astan... at gmail.com> wrote: > Good day, > > I can't prove, neither a la mano nor with Mathematica, > that this limit: > > Limit[Hypergeometric2F1[1,-2 j,j,-1/2]/Sqrt[j],j -> Infinity] > > is 1 > > Any help is welcome... > > -- > Valeri Astanoff Good day, If this asymptotic equivalence is correct, the limit should not be 1 but Sqrt[Pi/3]: In[1]:= h = (2^(-1-2j)*27^j*Gamma[1+j]*Gamma[1+2j])/Gamma[1+3j]; In[2]:= Limit[h/Sqrt[j], j -> Infinity] Out[2]= Sqrt[Pi/3] In[3]:= % // N Out[3]= 1.02333 -- v.a.