Basic hypergeometric series very well-poised in U(n) (Q1085316)

We introduce and study a U(n) multiple series generalization of classical very well-poised basic hypergeometric series of one variable. Two new multiple series generalizations of the terminating \({}_ 6\Phi_ 5\) summation theorem are derived. One of these extends to a U(n) generalization of the nonterminating \({}_ 6\Phi_ 5\) summation theorem. Multiple series generalizations of the summation theorems of Kummer and Dixon appear as special cases. We obtain the corresponding theorems for ordinary series by taking the limit as \(q\to 1\) of all these results.