Probabilistic degenerate Bernstein polynomials

• Published in: Applied mathematics in science and engineering Vol. 33; no. 1
• Main Authors: Wang, Jinyu, Ma, Yuankui, Kim, Taekyun, Kim, Dae San
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 31.12.2025
• Subjects: 11B68; 11B83; 60-08; Probabilistic degenerate Bernstein polynomials associated with Y
• ISSN: 2769-0911; 2769-0911
• DOI: 10.1080/27690911.2024.2448191

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.