Transformations of \(U(n+1)\) multiple basic hypergeometric series (Q2751976)

S.~C.~Milne has pioneered the theory of multiple basic hypergeometric series, and over the past two decades has written close to thirty papers on the subject. In this paper many of his (and coworkers') main discoveries are reviewed and the paper provides an excellent introduction to the field of multivariable basic hypergeometric series, with well over a hundred references to the recent and not-so-recent literature. Covered are, \(U(n+1)\) extensions to many of the classic summations and transformations for one-variable basic hypergeometric series, the \(U(n+1)\) Bailey transform and Bailey lemma, eta function identities, and Milne's recent major breakthrough on the classical sums of squares problem.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00054].