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

generalized hypergeometric function | nearly-poised | Saalschützian | well-poised