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

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 cal...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences 2021, Vol.129 (1), p.393-408
Main Authors: Jang, Lee-Chae, San Kim, Dae, Kim, Hanyoung, Kim, Taekyun, Lee, Hyunseok
Format: Article
Language:English
Subjects:
Calculus
Combinatorial analysis
Mathematical analysis
Polynomials
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Summary: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.
ISSN:1526-1506
1526-1492
1526-1506
DOI:10.32604/cmes.2021.016917