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Re: Annoying error in Hypergeometric2F1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107901] Re: [mg107888] Annoying error in Hypergeometric2F1
  • From: Christoph Lhotka <christoph.lhotka at univie.ac.at>
  • Date: Tue, 2 Mar 2010 07:52:59 -0500 (EST)
  • References: <201003020835.DAA03959@smc.vnet.net>

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



anguzman at 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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