Orthogonality Associated with Bessel-Type Sheffer Sequences with Q-Parameters

Certain orthogonal polynomials are involved in various problems occurring in probability, celestial mechanics, combinatorics, and other fields of theoretical and applied sciences. The article aims to introduce $q$-Sheffer sequences of Bessel type using $q$-Riordan matrices by means of the Eulerian generating function. Series expansion and determinant expressions are obtained for these $q$-sequences. We discuss the orthogonality of $q$-Sheffer sequences of Bessel type by establishing their three term $q$-recurrence relations. As applications, we obtain the Eulerian generating functions and other properties for some special $q$-Sheffer sequences of Bessel type including the continuous $q$-Hermite and $q$-exponential polynomials of Bessel type.