:-) Actually I do not know ... Bill Gosper has a large herd of matrix recursions ... But I guess it comes through the quadratic transformation by looking at the terms. And the closed curve should be the pre-image where the transformed series converges (ok, the boundary, which is the unit circle). But I have not tried it seriously :-( And he has some similar for the exceptional cases (Problem 2 in the link). Forrey is just for reference, he uses the classical linear transformations and his very point is to use careful finite differences for the exceptional cases (or close to them). However I think it is difficult to cover all the complex plane (example: unit circle intersecting diagonals), I think there are notes by Temme on that. But so far Forrey seems to have the best know (public, double precision) code, Temme occasionally stated that at the num analysis usenet group. So it is a good reference.

Being mostly in 'user mode' I understand Alex :-) And - Tim: your argumentation may be correct, but it does not give credit to different roles. If you are a 'programmer' you will be forced to follow concurrent SW needs. But as a user you want to apply the stuff (and even pay to get not being forced more then really necessary).

Being mostly in 'user mode' I understand Alex :-) And - Tim: your argumentation may be correct, but it does not give credit to different roles. If you are a 'programmer' you will be forced to follow concurrent SW needs. But as a user you want to apply the stuff (and even pay to get not being forced more then really necessary).

For example: I switch off the XP firewall (and several other stuff XP 'provides') and use ZoneAlarm instead. At first use of Maple it asks to allow Maple to act as server (it asks for mserver.exe, cwmaple.exe and maple.exe I think)

I changed the thread title a bit and added a "?"

Dave, Thank you for the detailled answer, it is very welcome. Certainly it would be worth to add such to the docu, especially for the numerics ... I was not aware of this rule in Maple. And also not of the subtility of the 'complex zero'. Please find attached the version for M10 and M11, printed as pdf. There seems to be a difference in handling 2.8 + 1e-300*I*0 giving 2.8 or 2.8 + 0.0*I (and after that it is covered by what you said).

Thank you, may be I am simply wrong with "limit from the upper plane". But would like to know. And I am embarrassed by answer M10 vs M11 test version.

I would say: one or the other result should be correct. Yes, it is to look at the brunch cut and the correct value for z in ]1 .. infinity[ is by the limit from the upper half plane I think, i.e. z = x + eps*I, 0 LT eps ~ 0. The value M10 gives is the limit from the lower half plane. It does not depend on the exactness of the parameters, my original values where

a=1.275676034060910+.4761860898177549*I, 
b=-2.620054215532604+.8547207931058080*I, 
c=-1.089001803619454+.7165427599546715*I,

As it costs me a *lot* of time to find a supposed error in a code I
would like to rant about Maple 10:

/ ranting on

 restart: Digits:=18:
 MPL_2F1:=proc(a,b,c, z) evalf(hypergeom([a,b],[c],z)); end proc:
 
 tstData:=[a=1.2+.4*I, b=-2.6+.85*I, c=-1.0+.7*I, z= 2.8];
 TstData:= op(eval([a,b,c,z], (tstData))):
 MPL_2F1(TstData);

             -720.102249494927486 + 440.743419599155560 I

 tstData:=[a=1.2+.4*I, b=-2.6+.85*I, c=-1.0+.7*I, z= 2.8 + 1e-3000*I];
 TstData:= op(eval([a,b,c,z], (tstData))):
 MPL_2F1(TstData);

             1.49139640953106626 - 3.74804421753558801 I

It is not very likely to be correct (using M10) and in M11 ~ the second
result is given.

/ranting off

i expect it to work in Maple 11 my PC is the same (having an Athlon), but i do not know the command which lets report Maple the detailled setting of the machine

yes, but i was testing some numerical code for floating point numbers by comparing to Maple

one applies Euler's transformation (Abramowitz et al, 15.3.3), the resulting hypergeom is a polynom (as one of the 'upper' entries is a negative natural number), so one can write down the explicit form

xp-antispy is, what i use to switch off all the dirt provided by MS + ZoneAlarm to have a firewall (ok, i am on M10, but anyway give that a try)

Very much appreciated! It would make life easier ...

sure, but Maple's marketing mgmt seems not want to understand that since years so the action should be at the side of Tom's Managing Dictator :-)