Combinatorial identities related to degenerate Stirling numbers of the second kind
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912182686449664 |
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| author | Kim, Taekyun Kim, Dae san |
| author_facet | Kim, Taekyun Kim, Dae san |
| contents | The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of this paper is to study some properties, certain identities, recurrence relations and explicit expressions for degenerate Stirling numbers of the second kind, which are a degenerate version of the Stirling numbers of the second kind. These numbers appear very frequently when we study various degenerate versions of many special polynomials and numbers. Especially, we consider some closely related polynomials and power series in connection with a degenerate version of Euler's formula for the Stirling numbers of the second kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial identities related to degenerate Stirling numbers of the second kind Kim, Taekyun Kim, Dae san Number Theory Combinatorics 11B68, 11B73, 11B83 The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of this paper is to study some properties, certain identities, recurrence relations and explicit expressions for degenerate Stirling numbers of the second kind, which are a degenerate version of the Stirling numbers of the second kind. These numbers appear very frequently when we study various degenerate versions of many special polynomials and numbers. Especially, we consider some closely related polynomials and power series in connection with a degenerate version of Euler's formula for the Stirling numbers of the second kind. |
| title | Combinatorial identities related to degenerate Stirling numbers of the second kind |
| topic | Number Theory Combinatorics 11B68, 11B73, 11B83 |
| url | https://arxiv.org/abs/2501.05696 |