A Second Type Of Higher Order Generalised Geometric Polynomials and Higher Order Generalised Euler Polynomials

Abstract

In this study we introduce a second type of higher order generalised geometric polynomials. This we achieve by examining the generalised stirling numbers $S(n;k;\alpha ;\beta ;\gamma )$ [Hsu & Shiue,1998] for some negative arguments. We study their number theoretic properties, asymptotic properties, and study their combinatorial properties using the notion of barred preferential arrangements. We also proposed a generalisation of the classical Euler polynomials and show how these Euler polynomials are related to the second type of higher order generalised geometric polynomials.

References in corpus (4)

• Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications
• Geometric Polynomials: Properties and Applications to Series with Zeta Values
• A study of a family of generating functions of Nelsen-Schmidt type and some identities on restricted barred preferential arrangements
• Generalised Barred Preferential Arrangements