Generalizations of generating functions for basic hypergeometric orthogonal polynomials

This is the authors' abstract. We don't add key points for this paper.

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.