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Probabilistic degenerate poly-Bell polynomials associated with random variables.

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Title: Probabilistic degenerate poly-Bell polynomials associated with random variables.
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]
Copyright of Mathematical & Computer Modelling of Dynamical Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Probabilistic degenerate poly-Bell polynomials associated with random variables.
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  Data: <searchLink fieldCode="AR" term="%22Xue%2C+Pengxiang%22">Xue, Pengxiang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ma%2C+Yuankui%22">Ma, Yuankui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mayuankui@xatu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Kim%2C+Taekyun%22">Kim, Taekyun</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> tkkim@kw.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Kim%2C+Dae+San%22">Kim, Dae San</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> dskim@sogang.ac.kr</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Wenpeng%22">Zhang, Wenpeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wpzhang888@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+%26+Computer+Modelling+of+Dynamical+Systems%22">Mathematical & Computer Modelling of Dynamical Systems</searchLink>. Dec2025, Vol. 31 Issue 1, p1-17. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink><br /><searchLink fieldCode="DE" term="%22Gamma+distributions%22">Gamma distributions</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Generating+functions%22">Generating functions</searchLink><br /><searchLink fieldCode="DE" term="%22Identities+%28Mathematics%29%22">Identities (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Binomial+distribution%22">Binomial distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink>
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Mathematical & Computer Modelling of Dynamical Systems is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/13873954.2025.2497367
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      – Code: eng
        Text: English
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        PageCount: 17
        StartPage: 1
    Subjects:
      – SubjectFull: Random variables
        Type: general
      – SubjectFull: Gamma distributions
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Stochastic processes
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      – SubjectFull: Generating functions
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      – SubjectFull: Identities (Mathematics)
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      – SubjectFull: Binomial distribution
        Type: general
      – SubjectFull: Exponential functions
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      – TitleFull: Probabilistic degenerate poly-Bell polynomials associated with random variables.
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            NameFull: Xue, Pengxiang
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            NameFull: Ma, Yuankui
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            NameFull: Kim, Taekyun
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            – D: 01
              M: 12
              Text: Dec2025
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              Y: 2025
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