QUAESTIONES MATHEMATICAE, vol.45, no.1, pp.71-89, 2022 (SCI-Expanded)
In this study we introduce a second type of higher order generalized geometric polynomials. This we achieve by examining the generalized stirling numbers S(n, k, alpha, beta, gamma) [Hsu and Shiue, 1998] for some negative arguments. We study their number theoretic properties, asymptotic properties, and their combinatorial properties using the notion of barred preferential arrangements. We also proposed a generalisation of the classical Euler polynomials and show how these generalized Euler polynomials are related to the second type of higher order generalized geometric polynomials.