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ARTICLE

Some Properties of Degenerate r-Dowling Polynomials and Numbers of the Second Kind

Hye Kyung Kim^1,*, Dae Sik Lee²

1 Department of Mathematics Education, Daegu Catholic University, Gyeongsan, 38430, Korea
2 School of Electronic and Electric Engineering, Daegu University, Gyeongsan, 38453, Korea

* Corresponding Author: Hye Kyung Kim. Email:

(This article belongs to the Special Issue: Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling)

Computer Modeling in Engineering & Sciences 2022, 133(3), 825-842. https://doi.org/10.32604/cmes.2022.022103

Received 21 February 2022; Accepted 11 May 2022; Issue published 03 August 2022

Abstract

The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics. In recent years, some mathematicians have studied degenerate version of them and obtained many interesting results. With this in mind, in this paper, we introduce the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind. We derive many interesting properties and identities for them including generating functions, Dobinski-like formula, integral representations, recurrence relations, differential equation and various explicit expressions. In addition, we explore some expressions for them that can be derived from repeated applications of certain operators to the exponential functions, the derivatives of them and some identities involving them.

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