A generalized hypergeometric function _p F_q[α_1, α_2, ..., α_p β_1, β_2, ..., β_q;z], is said to be Saalschützian if it is k-balanced with k = 1, sum_(i = 1)^q β_i = 1 + sum_(i = 1)^p α_i.

generalized hypergeometric function | k-balanced | nearly-poised | well-poised