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Probabilistic degenerate Stirling polynomials of the second kind and their applications

Author

Listed:
  • Taekyun Kim
  • Dae San Kim
  • Jongkyum Kwon

Abstract

The aim of this paper is to further study probabilistic versions of the degenerate Stirling polynomials of the second kind, namely the probabilistic degenerate Stirling polynomials of the second kind associated with $Y$Y, which are also degenerate versions of the probabilistic Stirling polynomials of the second kind investigated earlier. Here $Y$Y is a random variable whose moment generating function exists in some neighbourhood of the origin. We derive some properties, explicit expressions and certain identities for those polynomials. In addition, we apply our results to the Bernoulli random variable with probability of success $p$p, the normal random variable with parameters $\mu = 0,{\sigma ^2} = 1$μ=0,σ2=1, and to the uniform random variable on $(0,1)$(0,1).

Suggested Citation

  • Taekyun Kim & Dae San Kim & Jongkyum Kwon, 2024. "Probabilistic degenerate Stirling polynomials of the second kind and their applications," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 30(1), pages 16-30, December.
  • Handle: RePEc:taf:nmcmxx:v:30:y:2024:i:1:p:16-30
    DOI: 10.1080/13873954.2023.2297571
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