U(n) very-well-poised 10ط9 transformations

In this paper we derive multivariable generalizations of Baileyʹs classical terminating very-well-poised 10ط9 transformation. We work in the setting of multiple basic hypergeometric series very-well-poised on unitary groups U(n + 1). We obtain these U(n + 1) 10ط9 transformations from an alternate form of our general U(n + 1) classical Bailey transform, and the U(n + 1) generalizations of Jacksonʹs q-analog of Dougallʹs terminating 7F6(1) summation. One of these 10ط9 transformations contains the U(n + 1) 10ط9 transformation of Denis and Gustafson (1992) as a speci We also deduce a U(n + 1) extension of one of Sears 4ط3 transformations. The classical case of all this work corresponds to U(2), or equivalently A1.