Degenerate Eulerian polynomials and numbers
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910726776422400 |
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| author | Kim, Taekyun Kim, Dae san |
| author_facet | Kim, Taekyun Kim, Dae san |
| contents | The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian numbers, and to derive some of their properties. Specifically, we derive an identity, recursive relations, generating function and degenerate version of Worpitzky's identity for the degenerate Eulerian polynomials and numbers. In addition, we obtain several results involving the degenerate Stirling numbers of the second kind and the degenerate Bernoulli numbers as well as the degenerate Eulerian numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degenerate Eulerian polynomials and numbers Kim, Taekyun Kim, Dae san Number Theory 11B68, 11B73, 11B83 The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian numbers, and to derive some of their properties. Specifically, we derive an identity, recursive relations, generating function and degenerate version of Worpitzky's identity for the degenerate Eulerian polynomials and numbers. In addition, we obtain several results involving the degenerate Stirling numbers of the second kind and the degenerate Bernoulli numbers as well as the degenerate Eulerian numbers. |
| title | Degenerate Eulerian polynomials and numbers |
| topic | Number Theory 11B68, 11B73, 11B83 |
| url | https://arxiv.org/abs/2412.03119 |