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ARTICLE

Study of Degenerate Poly-Bernoulli Polynomials by λ-Umbral Calculus

by Lee-Chae Jang¹, Dae San Kim², Hanyoung Kim³, Taekyun Kim^3,*, Hyunseok Lee³

1 Graduate School of Education, Konkuk University, Seoul, 143-701, Korea
2 Department of Mathematics, Sogang University, Seoul, 121-742, Korea
3 Department of Mathematics, Kwangwoon University, Seoul, 139-701, Korea

* Corresponding Author: Taekyun Kim. Email:

(This article belongs to the Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2021, 129(1), 393-408. https://doi.org/10.32604/cmes.2021.016917

Received 09 April 2021; Accepted 13 May 2021; Issue published 24 August 2021

Abstract

Recently, degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee. The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed ‘λ-umbral calculus.’ In more detail, we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind, by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind, and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind.

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Citations