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Re: Hypergeometric2F1 gives wrong complex infinities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100954] Re: Hypergeometric2F1 gives wrong complex infinities
  • From: Sebastian <meznaric at gmail.com>
  • Date: Thu, 18 Jun 2009 20:46:22 -0400 (EDT)
  • References: <h19i96$p8o$1@smc.vnet.net> <h1a9qf$80l$1@smc.vnet.net>

On Jun 18, 9:50 am, "David W. Cantrell" <DWCantr... at sigmaxi.net>
wrote:
> pfalloon <pfall... 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 y=
et
> report different behaviors.
>
> David

I also get ComplexInfinity in version 7.0. Jens-Peer Juska you used a
different expression in your trial, but strange that Peter got a
correct result with simply using N[...].


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