The authors introduce a pair of canonical-conjugate q-deformed operators D, X and discuss the relations between the deformed operators D, X and q-series. The realizations of some Lie symmetries, Heisenberg and quantum Heisenberg algebras are given for the operators D and X. They show that the q-analogous Hermite polynomials are representations of Heisenberg and quantum Heisenberg algebras realized in this way. When q is a root of unity, the properties of the q-analogous Hermite polynomials are also discussed.