Study of Degenerate Poly-Bernoulli Polynomials by λ-Umbral Calculus
- Lee-Chae Jang1, Dae San Kim2, Hanyoung Kim3, Taekyun Kim3,*, 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 this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)
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 this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)
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.
Keywords
Degenerate poly-Bernoulli polynomials; degenerate polyexponential functions; λ-umbral calculus
Cite This Article
Jang, L., Kim, D. S., Kim, H., Kim, T., Lee, H. (2021). Study of Degenerate Poly-Bernoulli Polynomials by λ-Umbral Calculus. CMES-Computer Modeling in Engineering & Sciences, 129(1), 393–408.
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