Transformations of multiple q-series with quasi-arbitrary terms

The main object of this paper is to present several (presumably new) transf ormations of series whose terms involve basic (or q-) Pochhammer symbols to gether with an essentially arbitrary factor. Each of these general q-series transformations is shown to be related rather closely to a certain basic h ypergeometric summation or transformation formula. Relevant connections of many of the multiple q-series transformations with various known results ar e also considered briefly. (C) 1999 Academic Press.