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.
Keywords: 33C20; 33D45; basic hypergeometric functions; generating functions; q-polynomials.