Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912551642595328 |
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| author | Kim, Taekyun Kim, Dae San |
| author_facet | Kim, Taekyun Kim, Dae San |
| contents | Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and probabilistic degenerate Frobenius-Euler polynomials associated with Y , and more generally of their higher-order counterparts. We derive explicit formulas with the help of umbral calculus and illustrate our results in the case of several random variables Y |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials Kim, Taekyun Kim, Dae San Number Theory Probability 05A40, 11B68, 11B73, 60-08 Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and probabilistic degenerate Frobenius-Euler polynomials associated with Y , and more generally of their higher-order counterparts. We derive explicit formulas with the help of umbral calculus and illustrate our results in the case of several random variables Y |
| title | Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials |
| topic | Number Theory Probability 05A40, 11B68, 11B73, 60-08 |
| url | https://arxiv.org/abs/2508.17189 |