Some Basic Extensions of Gustafson-Rakha's Multivariate Basic Hypergeometric Series

In this paper we extend some special cases of the multivariate basic hypergeometric series associated to the roots system of type A_m A_m that has been established and proved in [8]. For both types of the series, we will prove that when m = 2n; n = 1 m = 2n; n =1 one of the series is equivalent to Jackson's ₈ Y₇ _8 Psi _7 sum, while the other series is equivalent to the basic Gauss' sum.