A second type of higher order generalized geometric polynomials and higher order generalized Euler polynomials. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Corcino, Cristina B.; Corcino, Roberto B.; Çekim, Bayram; Kargin, Levent; Nkonkobe, Sithembele
• Is Part Of: Quaestiones mathematicae. Volume 45:Issue 1(2022)
• Page Start: 71
• Page End: 89
• Publication Date: 2022-01-02
• Subjects: 05A15 -- 05A16 -- 05A18 -- 05A19 -- 11B73 -- 11B83; Preferential arrangement -- barred preferential arrangement -- geometric polynomial -- Euler polynomials; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2020.1848937
• Languages: English
• ISSNs: 1607-3606

Abstract

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, α, β, γ ) [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.