Notes on $q$-Hermite Based Unified Apostol Type Polynomials

Abstract

In this article, a new class of $q$-Hermite based unified Apostol type polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating methods. We also introduce $q$-analog of Stirling numbers of second kind of order $\nu$ by which we construct a relation including aforementioned polynomials.

Explicit formula of a new class of q-Hermite-based Apostol-type polynomials and generalization

“…Other interesting links about q-Hermite-based Apostol-type numbers, (p; q)-analogue type of Frobenius Genocchi numbers and polynomials and q-analogue of Hermite poly-Bernoulli numbers and polynomials are illustrated in the works [6][7][8][9][10][11] of Waseem A. Khan et al…”