Typically, you need to tell mpmath to use an appropriate precision for the evaluation:
mpmath.mp.dps http://bl-1.com/click/load/AzZebQZnUGVfPQNgU2Q-b0231= 300 float(mpmath.hyp2f1('10','5','-300.5','0.5')) -3.8520270815239185e+32
Oh k! I didn't pay that much heed to it and set mp.dpshttp://bl-1.com/click/load/UGVbaAdmUmdXNVU2U2c-b0231to 100. Wonder why the
difference was so drastic. Anyways thanks a lot.
***
What can help in hyp2f1 for large values of a,b,c is use of recurrence relations. These are typically stable in one direction only. [1] This seems to be still a partially open research question...
Our current hyp2f1 implementation does use recurrences (hyp2f1ra), but perhaps they are not invoked for this case. The problem here can be the accurate determination of the convergence region for each parameter value.
[1] http://www.ams.org/journals/mcom/2007-76-259/S0025-5718-07-01918-7/http://bl-1.com/click/load/BzIAM1c2UmcCYFU2U2Y-b0231
-- Pauli Virtanen
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