Degenerate Poly-Lah-Bell Polynomials and Numbers

Many mathematicians studied “poly” as a generalization of the well-known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly-Lah-Bell polynomials arising from the degenerate polyexponential f...

Full description

Saved in:
Bibliographic Details
Main Authors: Taekyun Kim, Hye Kyung Kim
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/2917943
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832563429751128064
author Taekyun Kim
Hye Kyung Kim
author_facet Taekyun Kim
Hye Kyung Kim
author_sort Taekyun Kim
collection DOAJ
description Many mathematicians studied “poly” as a generalization of the well-known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly-Lah-Bell polynomials arising from the degenerate polyexponential functions which are reduced to degenerate Lah-Bell polynomials when k=1. In particular, we call these polynomials the “poly-Lah-Bell polynomials” when λ⟶0. We give their explicit expression, Dobinski-like formulas, and recurrence relation. In addition, we obtain various algebraic identities including Lah numbers, the degenerate Stirling numbers of the first and second kind, the degenerate poly-Bell polynomials, the degenerate poly-Bernoulli numbers, and the degenerate poly-Genocchi numbers.
format Article
id doaj-art-55b5a3d065d14a89b40cce3e80904ee3
institution Kabale University
issn 2314-4785
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-55b5a3d065d14a89b40cce3e80904ee32025-02-03T01:20:11ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2917943Degenerate Poly-Lah-Bell Polynomials and NumbersTaekyun Kim0Hye Kyung Kim1Department of MathematicsDepartment of Mathematics EducationMany mathematicians studied “poly” as a generalization of the well-known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly-Lah-Bell polynomials arising from the degenerate polyexponential functions which are reduced to degenerate Lah-Bell polynomials when k=1. In particular, we call these polynomials the “poly-Lah-Bell polynomials” when λ⟶0. We give their explicit expression, Dobinski-like formulas, and recurrence relation. In addition, we obtain various algebraic identities including Lah numbers, the degenerate Stirling numbers of the first and second kind, the degenerate poly-Bell polynomials, the degenerate poly-Bernoulli numbers, and the degenerate poly-Genocchi numbers.http://dx.doi.org/10.1155/2022/2917943
spellingShingle Taekyun Kim
Hye Kyung Kim
Degenerate Poly-Lah-Bell Polynomials and Numbers
Journal of Mathematics
title Degenerate Poly-Lah-Bell Polynomials and Numbers
title_full Degenerate Poly-Lah-Bell Polynomials and Numbers
title_fullStr Degenerate Poly-Lah-Bell Polynomials and Numbers
title_full_unstemmed Degenerate Poly-Lah-Bell Polynomials and Numbers
title_short Degenerate Poly-Lah-Bell Polynomials and Numbers
title_sort degenerate poly lah bell polynomials and numbers
url http://dx.doi.org/10.1155/2022/2917943
work_keys_str_mv AT taekyunkim degeneratepolylahbellpolynomialsandnumbers
AT hyekyungkim degeneratepolylahbellpolynomialsandnumbers