Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators. In particular, we obtain two expressions for th...
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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/10.1155/2022/2626249 |
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| _version_ | 1832562420081491968 |
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| author | Taekyun Kim Dae San Kim Hye Kyung Kim |
| author_facet | Taekyun Kim Dae San Kim Hye Kyung Kim |
| author_sort | Taekyun Kim |
| collection | DOAJ |
| description | Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators. In particular, we obtain two expressions for the generating function of the degenerate r-Bell polynomials in z2, and a recurrence relation and Dobinski-like formula for the degenerate r-Bell numbers. These are derived from the degenerate normal ordering of a degenerate integral power of the number operator in terms of boson operators where the degenerate r-Stirling numbers of the second kind appear as the coefficients. |
| format | Article |
| id | doaj-art-9a240363a1bd45bfa2cb276ae3e61c95 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9a240363a1bd45bfa2cb276ae3e61c952025-02-03T01:22:41ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2626249Degenerate r-Bell Polynomials Arising from Degenerate Normal OrderingTaekyun Kim0Dae San Kim1Hye Kyung Kim2Department of MathematicsDepartment of MathematicsDepartment of Mathematics EducationRecently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators. In particular, we obtain two expressions for the generating function of the degenerate r-Bell polynomials in z2, and a recurrence relation and Dobinski-like formula for the degenerate r-Bell numbers. These are derived from the degenerate normal ordering of a degenerate integral power of the number operator in terms of boson operators where the degenerate r-Stirling numbers of the second kind appear as the coefficients.http://dx.doi.org/10.1155/2022/2626249 |
| spellingShingle | Taekyun Kim Dae San Kim Hye Kyung Kim Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering Journal of Mathematics |
| title | Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering |
| title_full | Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering |
| title_fullStr | Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering |
| title_full_unstemmed | Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering |
| title_short | Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering |
| title_sort | degenerate r bell polynomials arising from degenerate normal ordering |
| url | http://dx.doi.org/10.1155/2022/2626249 |
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