The q-Sheffer sequences of a new type and associated orthogonal polynomials

Using q-Riordan matrices in terms of the Eulerian generating functions we formulate the q-Sheffer sequences of a new type. This concept may differ from others in the literature appeared previously. We also give some conditions for q-Sheffer sequences to be orthogonal. As an application, we obtain the Eulerian generating functions for orthogonal polynomials of some special types. In addition, we consider interlacing properties for the zeros, particularly complex zeros of the orthogonal q-Sheffer sequence extending both the Hermite polynomials and the Chebyshev polynomials of the second kind.