Let generalized hypergeometric function _p F_q[α_1, α_2, ..., α_p β_1, β_2, ..., β_q;z] have p = q + 1. Then the generalized hypergeometric function is said to be nearly-poised of the first kind if β_1 + a_2 = ... = β_q + α_(q + 1). (omitting the initial equality in the definition for well-poised), and nearly-poised of the second kind if 1 + α_1 = β_1 + a_2 = ... = β_(q - 1) + α_q.

generalized hypergeometric function | k-balanced | Saalschützian