Probabilistic multi-Stirling numbers of the second kind and probabilistic multi-Lah numbers
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917708752224256 |
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| author | Kim, Taekyun Kim, Dae san |
| author_facet | Kim, Taekyun Kim, Dae san |
| contents | Assume that the moment generating function of the random vari able Y exists in a neighborhood of the origin. We introduce the probabilistic
multi-Stirling numbers of the second kind associated with Y and the proba bilistic multi-Lah numbers associated with Y, both of indices (k1,k2,...,kr), by
means of the multiple logarithm. Those numbers are respectively probabilistic
extensions of the multi-Stirling numbers of the second kind and the multi-Lah
numbers which, for (k1,k2,...,kr) = (1,1,...,1), boil down respectively to the
Stirling numbers of the second and the unsigned Lah numbers. The aim of this
paper is to study some properties, related identities, recurrence relations and
explicit expressions of those probabilistic extension numbers in connection with
several other special numbers |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic multi-Stirling numbers of the second kind and probabilistic multi-Lah numbers Kim, Taekyun Kim, Dae san Number Theory 11B68, 11B73, 11B83 Assume that the moment generating function of the random vari able Y exists in a neighborhood of the origin. We introduce the probabilistic multi-Stirling numbers of the second kind associated with Y and the proba bilistic multi-Lah numbers associated with Y, both of indices (k1,k2,...,kr), by means of the multiple logarithm. Those numbers are respectively probabilistic extensions of the multi-Stirling numbers of the second kind and the multi-Lah numbers which, for (k1,k2,...,kr) = (1,1,...,1), boil down respectively to the Stirling numbers of the second and the unsigned Lah numbers. The aim of this paper is to study some properties, related identities, recurrence relations and explicit expressions of those probabilistic extension numbers in connection with several other special numbers |
| title | Probabilistic multi-Stirling numbers of the second kind and probabilistic multi-Lah numbers |
| topic | Number Theory 11B68, 11B73, 11B83 |
| url | https://arxiv.org/abs/2407.00061 |