Axel Vogt schrieb:   
   >   
   > 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.   
   > >   
   >   
   > 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)   
   >   
      
   Yes, (-n,-n)? "Meromorphic" in c would really be quite simple; could   
   there be problems with that statement if b = c = -n? Something   
   logarithmic? And a correction: My text quoted above should have read:   
   the series for F1(a,-m;-n;z) "breaks off after the term involving   
   z^(-m)".   
      
   Of course I agree with the view that a CAS must carefully document its   
   behavior in borderline situations.   
      
   Martin.   
      
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