A second type of higher order generalized geometric polynomials and higher order generalized Euler polynomials


Corcino C. B. , Corcino R. B. , ÇEKİM B., KARGIN L., Nkonkobe S.

QUAESTIONES MATHEMATICAE, vol.45, no.1, pp.71-89, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.2989/16073606.2020.1848937
  • Journal Name: QUAESTIONES MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.71-89
  • Keywords: Preferential arrangement, barred preferential arrangement, geometric polynomial, Euler polynomials, GENERATING-FUNCTIONS, BERNOULLI, SERIES

Abstract

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.