Hiromasa Nakayama
hypergeo1.hypergeometric_pFq(list1.list(a, b, c),
list1.list(k - b, k - c), arith1.unary_minus(1))
=
((hypergeo0.gamma(k - b) * hypergeo0.gamma(k - c)) /
(hypergeo0.gamma(k - b - c) * hypergeo0.gamma(k)) *
hypergeo1.hypergeometric_pFq(
list1.list(b, c, k / 2 - (a / 2), 1 / 2 + (k / 2) - (a / 2)),
list1.list(k - a, k / 2, 1 / 2 + (k / 2)),
1));
Transformation of a nearly-poised series 3_F_2(-1)
@@ /. {a->1/2,b->1/3,c->1/5,k->1}