Elementary asymptotics for the Stirling numbers of the second kind: The central range
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910269234479104 |
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| author | Hwang, Hsien-Kuei Li, Chong-Yi Zacharovas, Vytas |
| author_facet | Hwang, Hsien-Kuei Li, Chong-Yi Zacharovas, Vytas |
| contents | We derive the local and central limit theorems for the Stirling numbers of the second kind by elementary means, obtaining as corollaries effective asymptotic estimates for the Bell numbers and for the moments of the distribution. We also develop asymptotic expansions along several directions, all based on a novel finite-differencing approach; this provides the first self-contained elementary justification of such expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29633 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Elementary asymptotics for the Stirling numbers of the second kind: The central range Hwang, Hsien-Kuei Li, Chong-Yi Zacharovas, Vytas Combinatorics Primary 05A16, Secondary 11B73, 60F05, 60C05, 41A60 We derive the local and central limit theorems for the Stirling numbers of the second kind by elementary means, obtaining as corollaries effective asymptotic estimates for the Bell numbers and for the moments of the distribution. We also develop asymptotic expansions along several directions, all based on a novel finite-differencing approach; this provides the first self-contained elementary justification of such expansions. |
| title | Elementary asymptotics for the Stirling numbers of the second kind: The central range |
| topic | Combinatorics Primary 05A16, Secondary 11B73, 60F05, 60C05, 41A60 |
| url | https://arxiv.org/abs/2605.29633 |