Hiromasa Nakayama
hypergeo1.hypergeometric2F1(a, 1 - a, c, 1 / 2)
=
((hypergeo0.gamma(c / 2) * hypergeo0.gamma((1 / 2) + (c / 2)))
/ (hypergeo0.gamma((c / 2) + (a / 2)) *
hypergeo0.gamma((1 / 2) + (c / 2) - (a / 2))));
Summation theorems for ordinary hypergeometric series
@@ /. {a->1/3,c->1/3}