Probabilistic heterogeneous Stirling numbers and Bell polynomials
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909990899417088 |
|---|---|
| author | Kim, Taekyun Kim, Dae San |
| author_facet | Kim, Taekyun Kim, Dae San |
| contents | Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and Lah-Bell. By integrating the heterogeneous framework of Kim and Kim with probabilistic extensions, we derive explicit formulas, Dobiński-like identities, and recurrence relations. We further establish connections to partial Bell polynomials and provide applications for Poisson and Bernoulli distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09964 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Probabilistic heterogeneous Stirling numbers and Bell polynomials Kim, Taekyun Kim, Dae San Number Theory Probability 11B73, 11B83, 60-08 Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and Lah-Bell. By integrating the heterogeneous framework of Kim and Kim with probabilistic extensions, we derive explicit formulas, Dobiński-like identities, and recurrence relations. We further establish connections to partial Bell polynomials and provide applications for Poisson and Bernoulli distributions. |
| title | Probabilistic heterogeneous Stirling numbers and Bell polynomials |
| topic | Number Theory Probability 11B73, 11B83, 60-08 |
| url | https://arxiv.org/abs/2601.09964 |