Some Generating Functions for q-Polynomials - Cohl, Howard S.; Costas-Santos, Roberto S.; Wakhare, Tanay V. (Symmetry (Basel), 2018)
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hypergeometric series 4 ϕ 5 , 5 ϕ 5 , 4 ϕ 3 , 3 ϕ 2 , 2 ϕ 1 , and q-Pochhammer symbols. Starting with our q-generating functions, we are also able to find some new classical generating functions for the Pasternack and Bateman polynomials.