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Abstract
Multiple basic hypergeometric series associated to the unitary group U ( n + 1 ) have been investigated by various authors. Many different types of such series exist in the literature. From several U ( n + 1 ) generalizations of q-Chu–Vandermonde summation theorem established by Milne [S.C. Milne, Balanced ϕ 2 3 summation theorems for U ( n ) basic hypergeometric series, Adv. Math. 131 (1997) 93–187], the purpose of this paper is to obtain several U ( n + 1 ) generalizations of the Kalnins–Miller transformation by applying the q-exponential operator technique.
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