Probabilistic degenerate Stirling numbers of the first kind and their applications
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916282631192576 |
|---|---|
| author | Kim, Taekyun Kim, Dae san |
| author_facet | Kim, Taekyun Kim, Dae san |
| contents | Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are constructed from the degenerate cumulant generating function of Y. They are a degenerate version of the probabilistic Stirling numbers of the first kind associated with Y, which were recently introduced by Adell-Benyi. We investigate some properties, related identities, recurrence relations and explicit expressions for those numbers. In addition, we apply our results to the special cases of normal and gamma random variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic degenerate Stirling numbers of the first kind and their applications Kim, Taekyun Kim, Dae san Combinatorics Number Theory Probability 11B68, 11B73, 11B83 Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are constructed from the degenerate cumulant generating function of Y. They are a degenerate version of the probabilistic Stirling numbers of the first kind associated with Y, which were recently introduced by Adell-Benyi. We investigate some properties, related identities, recurrence relations and explicit expressions for those numbers. In addition, we apply our results to the special cases of normal and gamma random variables. |
| title | Probabilistic degenerate Stirling numbers of the first kind and their applications |
| topic | Combinatorics Number Theory Probability 11B68, 11B73, 11B83 |
| url | https://arxiv.org/abs/2406.06945 |