sp.hyp2f1(10,5,-300.5,0.5) >>>>-6.5184949735e+156 The present implementation of the function in scipy, involves one Euler Transform followed by the application of Power Series (as a and b turn negative after Euler Transform is applied once). This most probably blows up the values of function as |c|>>>|a| or |b|. In one of the attempts to debug this the function hyp2f1 (when c<0; a,b>0; |c|>>a,b) was made to call hys2f1 (power series) without Euler Transformation. The result was the same as what mpmath gives when the precision is less (~100), as the error tolerance for hys2f1 is high. (MACHEP of order 10^-17). On increasing the sensitivity by changing the local tolerance to the order of 10^-200, it works perfect.
What are the implications of adopting this method in the cases where hyp2f1 fails to give accurate results? Except of course the fact that this implementation would be heavy. > 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. > > The straight-forwardness of power series and its resemblance to mpmath tempted me to first try with hys2f1, However I have a strong feeling that owing to strong sensitivity of recurrence function in general, the implementation will be much faster. However direct implementation without a change in sensitivity fails to give the required answer. Regards Jenny > > -- > Pauli Virtanen > > >
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