A certain class of q-series transformations

A large number of summation and transformation formulas for a certain class of double hypergeometric series are observed here to follow fairly readily from a single known result which, in turn, is a very special case of one of six general expansion formulas given in the literature. Generalizations and unifications of these expansion formulas involving series with essentially arbitrary terms are presented. It is also shown how the various series transformations considered in this paper admit themselves of $\text{q}$-extensions which are capable of unifying numerous scattered results in the theory of basic double hypergeometric functions.