2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76763We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2ϕ_1$ transformation, the $q$-Pfaff-Kummer and Euler transformations, the $q$-Saalschütz summation formula and Sear's transformation for terminating, balanced ${}_4ϕ_3$ series. For bilateral series, we rederive Kaneko's analogue of the ${}_1ψ_1$ summation formula and give multivariable extensions of Bailey's ${}_2ψ_2$ transformations.Latex2e, 17 pagesQuantum AlgebraClassical Analysis and ODEstext