Probabilistic degenerate poly-Bell polynomials associated with random variables.
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| Title: | Probabilistic degenerate poly-Bell polynomials associated with random variables. |
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| Authors: | Xue, Pengxiang1 (AUTHOR), Ma, Yuankui1 (AUTHOR) mayuankui@xatu.edu.cn, Kim, Taekyun1,2 (AUTHOR) tkkim@kw.ac.kr, Kim, Dae San3 (AUTHOR) dskim@sogang.ac.kr, Zhang, Wenpeng1 (AUTHOR) wpzhang888@163.com |
| Source: | Mathematical & Computer Modelling of Dynamical Systems. Dec2025, Vol. 31 Issue 1, p1-17. 17p. |
| Subjects: | Random variables, Gamma distributions, Polynomials, Stochastic processes, Generating functions, Identities (Mathematics), Binomial distribution, Exponential functions |
| Abstract: | Let $Y$ Y be a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable $Y$ Y , arising from the degenerate polyexponential functions, which are probabilistic extensions of degenerate versions of the poly-Bell polynomials. We derive several explicit expressions and some related identities for them. In addition, we consider the special cases that $Y$ Y is the Bernoulli random variable with probability of success $p$ p or the gamma random variable with shape parameter 1 and scale parameter 1. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Let $Y$ Y be a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable $Y$ Y , arising from the degenerate polyexponential functions, which are probabilistic extensions of degenerate versions of the poly-Bell polynomials. We derive several explicit expressions and some related identities for them. In addition, we consider the special cases that $Y$ Y is the Bernoulli random variable with probability of success $p$ p or the gamma random variable with shape parameter 1 and scale parameter 1. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 13873954 |
| DOI: | 10.1080/13873954.2025.2497367 |
