Some q-generating functions of the Carlitz and Srivastava–Agarwal types associated with the generalized Hahn polynomials and the generalized Rogers–Szegö polynomials

Motivated essentially by the fact that generating functions play an important rôle in the investigation of many potentially useful properties of the sequences which they generate, various families of q-generating functions of the Carlitz and Srivastava–Agarwal types have been investigated in the literature for the continuous q-Hermite polynomials, the Hahn polynomials, the Rogers–Szegö polynomials, and indeed also for many other q-polynomial systems. The main object of this paper is to apply a certain q-exponential decomposition technique with a view to deriving several bilinear and trilinear q-generating functions associated with the generalized Hahn polynomials. As a simple consequence of one of the main results derived in this paper, we are led naturally to the corrected version of a bilinear q-generating function which appeared in one of Carlitz’s papers.