restart; interface(version);

  Classic Worksheet Interface, Maple 10.06, Windows, Oct 2 2006 Build ID 255401


expr:=hypergeom([1-I*a,1-I*b],[1],x);
convert(expr, hypergeom, "lower c");

            expr := hypergeom([1 - a I, 1 - b I], [1], x)

                                  0

Digits:=14:
subs(a=1, b=2, c=1, expr):
eval(%,x=2); evalf(%);
#Re(%%%); plot( %, x=-1..0.9); plot( %%, x=1.1 .. 3);

                 hypergeom([1 - I, 1 - 2 I], [1], 2)

               0.010385802579659 + 0.068521539093061 I

I would expect, that evalhf works for that without 'manual' translation ...

restart;
interface(version);

  Classic Worksheet Interface, Maple 10.06, Windows, Oct 2 2006 Build ID 255401


tst1:=proc(a,z) (-z)^(-a); end proc:
evalhf(tst1(1.5, 2.5));

  Error, fractional power of a negative


'(-z)^(-a)': '%'= convert(%,exp);
 
tst2:=proc(a,z) exp(-a*ln(-z)); end proc:
evalhf(tst2(1.5, 2.5));

                          (-a)
                      (-z)     = exp(-ln(-z) a)

                                 -9
          0.155662521299999988 10   + 0.252982212799999995 I

Should penguins wear coats at these times? - Yes ... but please ... those shoes ... Can we have recipes for fine French meals? - Yes ... and include canteen food! How about everything but Maple stuff here? - Yes, that's the primal intention ... Must one clutter up this board? Hm ... Seems to be 'Le Must' ... Lehalle, please stop your nonsense postings, the tracker shows all of this flood. Regards, Axel

Playing with numerics for the hypergeometric function 2F1 i stumbled into the following exactness stuff, where lots of digits are lost and one needs to increase working precision quite a lot to get a good answer: f1 and f2 result from evaluating ugly, but usual transcendent functions, f3 comes through high precision and f0 is the limiting case.

  restart;
  
  hypergeom([1,2+epsilon],[3],z): 
  '%' = simplify(convert(%,StandardFunctions));
  theSol1:=rhs(%): 
  
  theSol1 = -2*(z*(1-z)^epsilon*epsilon-1+(1-z)^epsilon)/
    z^2/((1-z)^epsilon)/epsilon/(1+epsilon);
  is(%);

Occasionally Maple does not make me happy, if I want numerical integrals with more than the 14 digits which are supplied through the NAG libraries - that may be rather slow. So I wrote my own solution using LCC-WIN32 (a (free) compiler system allowing 104 decimal points of precision), where I coded the double exponential integration method. That gives me what I want to have in reasonable time. Details are sketched in the uploaded zip-file (it contains all what is needed to run the stuff). Some draw-back: this is for Windows only and because of OpenMaple at least Maple 9 is need.