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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.