Probabilistic degenerate Bernstein polynomials
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866910635367858176 |
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| author | Wang, Jinyu Ma, Yuankui Kim, Taekyun Kim, Dae San |
| author_facet | Wang, Jinyu Ma, Yuankui Kim, Taekyun Kim, Dae San |
| contents | In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic degenerate Bernstein polynomials associated with Y which are both probabilistic extension of the degenerate Bernstein polynomials and degenerate version of the probabilistic Bernstein polynomials associated with $Y$. We derive several explicit expressions and certain related identities for those polynomials. In addition, we treat the special cases of the Poisson random variable, the Bernoulli random variable and of the binomial random variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic degenerate Bernstein polynomials Wang, Jinyu Ma, Yuankui Kim, Taekyun Kim, Dae San Number Theory Probability 11B68, 11B83, 60-08 In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic degenerate Bernstein polynomials associated with Y which are both probabilistic extension of the degenerate Bernstein polynomials and degenerate version of the probabilistic Bernstein polynomials associated with $Y$. We derive several explicit expressions and certain related identities for those polynomials. In addition, we treat the special cases of the Poisson random variable, the Bernoulli random variable and of the binomial random variable. |
| title | Probabilistic degenerate Bernstein polynomials |
| topic | Number Theory Probability 11B68, 11B83, 60-08 |
| url | https://arxiv.org/abs/2410.04464 |