Probabilistic degenerate Bernstein polynomials
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 generat...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2024.2448191 |
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| _version_ | 1841527917308280832 |
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| author | Jinyu Wang Yuankui Ma Taekyun Kim Dae San Kim |
| author_facet | Jinyu Wang Yuankui Ma Taekyun Kim Dae San Kim |
| author_sort | Jinyu Wang |
| collection | DOAJ |
| description | 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 neighbourhood 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 | Article |
| id | doaj-art-a25f43891f2f4f86be2453138ce9e66b |
| institution | Kabale University |
| issn | 2769-0911 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj-art-a25f43891f2f4f86be2453138ce9e66b2025-01-15T04:22:43ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112025-12-0133110.1080/27690911.2024.2448191Probabilistic degenerate Bernstein polynomialsJinyu Wang0Yuankui Ma1Taekyun Kim2Dae San Kim3School of Science, Xi'an Technological University, Xi'an, Shaanxi, People's Republic of ChinaSchool of Science, Xi'an Technological University, Xi'an, Shaanxi, People's Republic of ChinaSchool of Science, Xi'an Technological University, Xi'an, Shaanxi, People's Republic of ChinaDepartment of Mathematics, Sogang University, Seoul, Republic of KoreaIn 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 neighbourhood 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.https://www.tandfonline.com/doi/10.1080/27690911.2024.2448191Probabilistic degenerate Bernstein polynomials associated with Y11B6811B8360-08 |
| spellingShingle | Jinyu Wang Yuankui Ma Taekyun Kim Dae San Kim Probabilistic degenerate Bernstein polynomials Applied Mathematics in Science and Engineering Probabilistic degenerate Bernstein polynomials associated with Y 11B68 11B83 60-08 |
| title | Probabilistic degenerate Bernstein polynomials |
| title_full | Probabilistic degenerate Bernstein polynomials |
| title_fullStr | Probabilistic degenerate Bernstein polynomials |
| title_full_unstemmed | Probabilistic degenerate Bernstein polynomials |
| title_short | Probabilistic degenerate Bernstein polynomials |
| title_sort | probabilistic degenerate bernstein polynomials |
| topic | Probabilistic degenerate Bernstein polynomials associated with Y 11B68 11B83 60-08 |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2024.2448191 |
| work_keys_str_mv | AT jinyuwang probabilisticdegeneratebernsteinpolynomials AT yuankuima probabilisticdegeneratebernsteinpolynomials AT taekyunkim probabilisticdegeneratebernsteinpolynomials AT daesankim probabilisticdegeneratebernsteinpolynomials |