Transformations of multiple \(q\)-series with quasi-arbitrary terms (Q1283009)

The object of this paper is to obtain several new transformations and reduction formulas for multiple series whose terms involve basic (or \(q\)-) Pochhammer symbols and an essentially arbitrary factor. The series considered here are, in general, \(2r\)- and \(r\)-dimensional. Each of these series is shown to be related to a certain basic hypergeometric summation or transformation formula. Relevant connections of many of the multiple \(q\)-series transformations with various known results are also mentioned briefly.