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Probabilistic multi-Stirling numbers of the second kind associated with random variables.

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Title: Probabilistic multi-Stirling numbers of the second kind associated with random variables.
Authors: Liu, Xiangjing1 (AUTHOR), Ma, Yuankui1 (AUTHOR), Kim, Taekyun2 (AUTHOR) tkkim@kw.ac.kr, Kim, Dae San3 (AUTHOR) tkkim@kw.ac.kr, Hei, Yanan1 (AUTHOR)
Source: Applied Mathematics in Science & Engineering. Dec2025, Vol. 33 Issue 1, p1-13. 13p.
Subjects: Random variables, Gamma distributions, Stochastic processes, Binomial distribution
Abstract: This paper investigates a probabilistic extension of the multi-Stirling numbers of the second kind and a 'poly' version of the probabilistic degenerate Lah-Bell polynomials. The probabilistic multi-Stirling numbers of the second kind are defined with respect to a random variable satisfying specific moment conditions, generalizing previous work on probabilistic Stirling numbers of the second kind. Explicit expressions and related identities are derived, including special cases where the random variable follows a gamma or Bernoulli distribution. Furthermore, probabilistic degenerate poly-Lah-Bell polynomials are introduced and their explicit expressions are obtained. [ABSTRACT FROM AUTHOR]
Copyright of Applied Mathematics in Science & Engineering 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 multi-Stirling numbers of the second kind associated with random variables.
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  Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+in+Science+%26+Engineering%22">Applied Mathematics in Science & Engineering</searchLink>. Dec2025, Vol. 33 Issue 1, p1-13. 13p.
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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="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Binomial+distribution%22">Binomial distribution</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper investigates a probabilistic extension of the multi-Stirling numbers of the second kind and a 'poly' version of the probabilistic degenerate Lah-Bell polynomials. The probabilistic multi-Stirling numbers of the second kind are defined with respect to a random variable satisfying specific moment conditions, generalizing previous work on probabilistic Stirling numbers of the second kind. Explicit expressions and related identities are derived, including special cases where the random variable follows a gamma or Bernoulli distribution. Furthermore, probabilistic degenerate poly-Lah-Bell polynomials are introduced and their explicit expressions are obtained. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Applied Mathematics in Science & Engineering 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: 10.1080/27690911.2025.2561683
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      – Code: eng
        Text: English
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      – SubjectFull: Gamma distributions
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      – SubjectFull: Stochastic processes
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      – SubjectFull: Binomial distribution
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              M: 12
              Text: Dec2025
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