Certain Bibasic Hypergeometric Transformation Formulae and Their Application to Rogers]Ramanujan Identities

In this paper, a variety of generalized bibasic hypergeometric transformation formulae have been investigated with the objective of finding a multiple series generalized Rogers]Ramanujan type of identity. It has been shown that some very interesting new multiple series identities of the Rogers]Ramanujan type can be found where there is more than one infinite product in which the terms in each product advance in different powers of q.