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Re: Annoying error in Hypergeometric2F1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107902] Re: Annoying error in Hypergeometric2F1
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Tue, 2 Mar 2010 07:53:10 -0500 (EST)
  • References: <hmikv0$55f$1@smc.vnet.net>

anguzman at ing.uchile.cl schrieb:
> 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
>

The Hypergeometric 2F1(a,b,c,z) has logarithmic branch points at z=+-1. 
That follows immediately using your expression by

In: TrigToExp[ArcTanh[x]]
Out: -(1/2) Log[1 - x] + 1/2 Log[1 + x]

Without assumptions you cannot use it for real |z|>1.
Probably you even don't know the actual meaning of the expression of yours.

Consider

In: Assuming[{x, y} > 1,
  FullSimplify@Hypergeometric2F1[1/2, 2, 3/2, x + I y]]


Out: 1/2 (1/(1 - x - I y) + ArcTanh[Sqrt[x + I y]]/Sqrt[x + I y])

In: % /. {x -> -125/100, y -> 0} // N

Out: 0.59836

-- 

Roland Franzius







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