[SciPy-dev] scipy.special.hyp2f1 bug?

[Skipper Seabold]

Since y'all are looking at the distributions vs. mpmath, it reminded
me of this.  I haven't filed a bug report yet, but I don't think one
existed when I found this.

I was working with the connection between the incomplete beta function
and the hypergeometric2f1 function in scipy.special for GLM in
statsmodels and I came across this blog post on mpmath about some
corner cases for the hypergeometric2f1.

<http://fredrik-j.blogspot.com/2009/06/hypergeometric-2f1-incomplete-beta.html>

Two examples of discrepancies.

In [1]: import mpmath

In [2]: from scipy import special

In [3]: mpmath.hyp2f1(3,-1,-1,0.5)
Out[3]: mpf('2.5')

In [4]: special.hyp2f1(3,-1,-1,.5)
Out[4]: 8.0

In [5]: mpmath.hyp2f1(1,1,4,3+4j)
Out[5]: mpc(real='0.49234384000963544', imag='0.60513406166123973')

In [6]: special.hyp2f1(1,1,4,3+4j)
Out[6]: (0.65925460474847919+1.3277887264473263j)

I will file a bug report shortly, if we think mpmath is correct vs. scipy.

-Skipper