Probabilistic derangement numbers and polynomials
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909065136832512 |
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| author | Kim, Taekyun Kim, Dae San |
| author_facet | Kim, Taekyun Kim, Dae San |
| contents | Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the derangement polynomials, the derangement polynomials of type 2 and the r-derangement numbers, namely the probabilistic derangement polynomials associated with Y, the probabilistic derangement polynomials of type 2 associated with Y and the probabilistic r-derangement numbers associated Y, respectively. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. In addition, we consider the special case that Y is the gamma random variable with parameters α,\b{eta} > 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic derangement numbers and polynomials Kim, Taekyun Kim, Dae San Probability Number Theory 11B73, 11B83 Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the derangement polynomials, the derangement polynomials of type 2 and the r-derangement numbers, namely the probabilistic derangement polynomials associated with Y, the probabilistic derangement polynomials of type 2 associated with Y and the probabilistic r-derangement numbers associated Y, respectively. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. In addition, we consider the special case that Y is the gamma random variable with parameters α,\b{eta} > 0. |
| title | Probabilistic derangement numbers and polynomials |
| topic | Probability Number Theory 11B73, 11B83 |
| url | https://arxiv.org/abs/2401.03986 |