Transformations of Multipleq-Series with Quasi-Arbitrary Terms

The main object of this paper is to present several (presumably new) transformations of series whose terms involve basic (orq-) Pochhammer symbols together with an essentially arbitrary factor. Each of these generalq-series transformations is shown to be related rather closely to a certain basic hypergeometric summation or transformation formula. Relevant connections of many of the multipleq-series transformations with various known results are also considered briefly.