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