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From: Alexandre Schmidt on 3 Mar 2010 05:51
You need to carry out an analytic continuation in order to write a
(convergent) Hypergeometric2F1 in the region |z|>1.
The formulas are well-known, as you can see in

L.J.Slater, "Generalized Hypergeometric Functions",
Y.L.Luke, "Mathematical Functions and Their Approximations"
or even in Gradsteyn and Rhyzik "Table of Integrals and Series".

Best regards,
Alexandre Schmidt
UFF
Brazil

On Mar 2, 10:02 am, Christoph Lhotka <christoph.lho...(a)univie.ac.at>
wrote:
> sorry, but neither with V5, V6 or V7 I could reproduce your result. I get:
>
> In[1]:= Hypergeometric2F1[1/2, 2, 3/2, -125/100]
>
> Sqrt[5]
> 10 + 9 Sqrt[5] ArcTan[-------]
> 2
> Out[1]= -------------------------------
> 45
>
> In[2]:= %//N
>
> Out[2]= 0.59836
>
> In[3]:= Hypergeometric2F1[1/2, 2, 3/2, -1.25]
>
> Out[3]= 0.59836
>
> (the ArcTan instead of the ArcTanh)
>
> Another question: I remember a definition, where 2F1(a,b,c,x) is defined
> only for |x|<1. Does anybody know why / about the generalization?
>
> chr
>
>
>
> anguz...(a)ing.uchile.cl wrote:
> > This is very bad and disappointing...what about version 7 ..
> > Looks like the symbolic evaluation is messed up..
>
> > Mathematica 6.0 for Linux x86 (32-bit)
> > Copyright 1988-2008 Wolfram Research, Inc.
>
> > In[1]:= Hypergeometric2F1[1/2, 2, 3/2, -125/100]
>
> > Sqrt[5]
> > 10 + 9 Sqrt[5] ArcTanh[-------]
> > =
2
> > Out[1]= -------------------------------
> > 45
>
> > In[2]:= %//N
>
> > Out[2]= 0.867836 - 0.702481 I
>
> > In[3]:= Hypergeometric2F1[1/2, 2, 3/2, -1.25]
>
> > Out[3]= 0.59836
>
> > Atte. Andres Guzman
>
> > ----------------------------------------------------------------
> > This message was sent using IMP, the Internet Messaging Program.
>
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