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...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2917943 |
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| 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 |