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 (SCI-Expanded) 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 (SCI-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
  • Gazi University Affiliated: Yes

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.