The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written c_(k + 1)/c_k = (P(k))/(Q(k)) = ((k + a_1)(k + a_2)...(k + a_p))/((k + b_1)(k + b_2)...(k + b_q)(k + 1)).

Carlson's theorem | Clausen formula | confluent hypergeometric function of the first kind | confluent hypergeometric limit function | Dixon's theorem | Dougall-Ramanujan identity | Dougall's theorem | generalized hypergeometric differential equation | Gosper's algorithm | hypergeometric function | hypergeometric identity | hypergeometric series | Jackson's identity | Kampé de Fériet function | k-balanced | Kummer's theorem | Lauricella functions | nearly-poised | q-hypergeometric function | Ramanujan's hypergeometric identity | Saalschützian | Saalschütz's theorem | Sister Celine's method | Slater's formula | Thomae's theorem | Watson's theorem | well-poised | Whipple's identity | Whipple's transformation | Wilf-Zeilberger pair | Zeilberger's algorithm