Hiromasa Nakayama
logic1.implies(
logic1.or(set1.in(arith1.unary_minus(b), setname1.N),
logic1.or(set1.in(arith1.unary_minus(c), setname1.N),
set1.in(arith1.unary_minus(d), setname1.N))),
hypergeo1.hypergeometric_pFq(list1.list(a, b, c, d),
list1.list(1 + a - b, 1 + a - c, 1 + a - d), 1)
=
((hypergeo0.gamma(1 + a - b) * hypergeo0.gamma(1 + a - c) *
hypergeo0.gamma(1 + a - d) * hypergeo0.gamma(1 + a - b - c - d))
/
(hypergeo0.gamma(1 + a - c - d) * hypergeo0.gamma(1 + a - b - c) *
hypergeo0.gamma(1 + a - b - d) * hypergeo0.gamma(1 + a))
*
hypergeo1.hypergeometric_pFq(
list1.list(1 / 2, b, c, d),
list1.list(1 + (a / 2), 1 / 2 + (a / 2), b + c + d - a),
1)));
Transformation of a nearly-poised series 4_F_3(1)
@@ /. {a->1/2,b->1/5,c->1/3,d->-2}