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Re: Hypergeometric2F1 gives wrong complex infinities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100902] Re: Hypergeometric2F1 gives wrong complex infinities
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Thu, 18 Jun 2009 04:50:11 -0400 (EDT)
  • References: <h19i96$p8o$1@smc.vnet.net> <h1a9qf$80l$1@smc.vnet.net>

pfalloon <pfalloon at gmail.com> wrote:
> On Jun 17, 11:52 am, Wieland Brendel <wielandbren... at gmx.net> wrote:
> > Dear all!
> > I currently have a problem with the hypergeometric function: Consider
> >
> > Hypergeometric2F1[1, I, I + 1, -Exp[a]]
> >
> > Whenever I set a > 36 I only get "complex infinity" as a result
> > although it should be perfectly finite (take 10 as a scale). Is there
> > any way to expand the range of a to higher values?
> >
> > I would be very thankful for a solution! A big thanks in advance and
> > best greetings from germany!
> >
> > Wieland Brendel
> >
> > PS: I use Mathematica 7.
>
> Hi Wieland,
>
> I don't see the problem you report:
>
> In[260]:= $Version
>
> Out[260]= 7.0 for Microsoft Windows (32-bit) (February 18, 2009)
>
> In[262]:= Hypergeometric2F1[1, I, I+1, -Exp[#]] & /@ {35,36,37,100} //
> N
>
> Out[262]= {-0.245831+0.116478 I, -0.0348098+0.269793 I,
> 0.208215+0.175061 I, 0.234576+0.137746 I}
>
> Can you reproduce the problem, showing the exact input?
>
> Cheers,
> Peter.

Using your In[262], version 6.0 for Windows gives ComplexInfinity for the
last two parts of the output. A simple way to avoid that behavior is to
specify an appropriate n-digit precision for N. For example:

In[8]:= x37 = Hypergeometric2F1[1, I, I + 1, -Exp[37]]

Out[8]= Hypergeometric2F1[1, I, 1 + I, -E^37]

In[9]:= N[x37]

Out[9]= ComplexInfinity

In[10]:= N[x37, 6]

Out[10]= 0.208215 + 0.175061 I

What puzzles me is that Wieland and Peter are both using version 7, and yet
report different behaviors.

David


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