Article ID: MTJPAM-D-23-00017

Title: Unification of the generating functions for Sheffer type sequences and their applications


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00017; Volume 5 / Issue 2 / Year 2023, Pages 71-88

Document Type: Research Paper

Author(s): Irem Kucukoglu a

aDepartment of Engineering Fundamental Sciences, Alanya Alaaddin Keykubat University TR-07425 Antalya, Turkey

Received: 26 July 2023, Accepted: 25 December 2023, Published: 31 December 2023

Corresponding Author: Irem Kucukoglu (Email address: irem.kucukoglu@alanya.edu.tr)

Full Text: PDF

Abstract

In this paper, it is aimed to introduce a unification and generalization of the generating functions for Sheffer type sequences such as the Peters polynomials, the Boole polynomials, the Changhee polynomials, the Korobov polynomials of the first kind and the Peters-type Simsek numbers and polynomials. Moreover, by considering a special case of the aforementioned unification, we also introduce and investigate a new family of numbers and polynomials to be referred as the more general kind of the Peters-type Simsek numbers and polynomials. Finally, we give some applications of our findings.

Keywords: Generating functions, special functions, special numbers and polynomials, Fibonacci type numbers and polynomials, Sheffer sequences, Peters-type Simsek numbers and polynomials, computation formulas, recurrence relations

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