Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915574580248576 |
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| author | Kim, Dae san Kim, Taekyun |
| author_facet | Kim, Dae san Kim, Taekyun |
| contents | We investigate the representation of arbitrary polynomials using probabilistic Bernoulli and degenerate Bernoulli polynomials associated with a random variable $Y$, whose moment generating function exists in a neighborhood of the origin. In addition, this paper explores the problem of representing arbitrary polynomials in terms of their higher-order counterparts. We develop explicit formulas for those representations with the help of umbral calculus and illustrate our results for several discrete and continuous random variables Y. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials Kim, Dae san Kim, Taekyun Number Theory Probability 05A19, 05A40, 11B68, 11B73, 11B83, 60-08 We investigate the representation of arbitrary polynomials using probabilistic Bernoulli and degenerate Bernoulli polynomials associated with a random variable $Y$, whose moment generating function exists in a neighborhood of the origin. In addition, this paper explores the problem of representing arbitrary polynomials in terms of their higher-order counterparts. We develop explicit formulas for those representations with the help of umbral calculus and illustrate our results for several discrete and continuous random variables Y. |
| title | Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials |
| topic | Number Theory Probability 05A19, 05A40, 11B68, 11B73, 11B83, 60-08 |
| url | https://arxiv.org/abs/2510.21558 |