From: &noreply@axelvogt.de   
      
   On 28.07.2014 21:10, clicliclic@freenet.de wrote:   
   >   
   > clicliclic@freenet.de schrieb:   
   >>   
   >> Let m,n be nonnegative integer numbers. The condition m> 2F1(a,-m;-n;z) to make sense follows from the series definition: the   
   >> hypergeometric series breaks off after the term involving z^(-n), and   
   >> terms must not become infinite up to that point. The condition   
   >> naturally extends to m=n with 2F1(a,-n;-n;z) = 1F0(a;z), which remains   
   >> an infinite series, however. There is no reason for Maple not to   
   >> implement this case too, for any pFq.   
   >>   
   >   
   > I should have looked more carefully: Maple seems to be doing just that,   
   > so that its hypergeom([1,-n],[-n],.5) ---> 2 would be a perfectly valid   
   > choice, whereas Mathematica seems to be doing something else, presumably   
   > equally valid. My guess is that analytic continuation here depends on   
   > the direction along which the point (-m,-n) is approached in (b,c)   
   > space.   
   >   
   > Martin.   
      
      
   I miss the time for the discussion, but Lebedev in Special Function says:   
      
   (in § 9.4):         It follows that for fixed z in the plane cut   
   along [1, oo], the hypergeometric function F(a,b;c; z) is an entire function   
   of a and b, and a meromorphic function of c, with simple poles at the points   
   c = 0, - 1, - 2, . . .   
      
   So it seems it is how to approach that point (b,c) = (-n,n)   
      
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