27 May 2024 | Lingling Luo, Taekyun Kim, Dae San Kim & Yuankui Ma
The article "Probabilistic degenerate Bernoulli and degenerate Euler polynomials" by Lingling Luo, Taekyun Kim, Dae San Kim, and Yuankui Ma introduces and studies the probabilistic extensions of degenerate Bernoulli and degenerate Euler polynomials. The authors define probabilistic degenerate Bernoulli polynomials and probabilistic degenerate Euler polynomials associated with a random variable \( Y \). They also introduce probabilistic degenerate \( r \)-Stirling numbers of the second kind and probabilistic degenerate two-variable Fubini polynomials associated with \( Y \). The paper derives properties, explicit expressions, recurrence relations, and identities for these polynomials and numbers. Special cases of \( Y \) include the gamma random variable, the Poisson random variable, and the Bernoulli random variable. The authors provide detailed proofs and examples to illustrate the theoretical results. The article is published in *Mathematical and Computer Modelling of Dynamical Systems* and is available online.The article "Probabilistic degenerate Bernoulli and degenerate Euler polynomials" by Lingling Luo, Taekyun Kim, Dae San Kim, and Yuankui Ma introduces and studies the probabilistic extensions of degenerate Bernoulli and degenerate Euler polynomials. The authors define probabilistic degenerate Bernoulli polynomials and probabilistic degenerate Euler polynomials associated with a random variable \( Y \). They also introduce probabilistic degenerate \( r \)-Stirling numbers of the second kind and probabilistic degenerate two-variable Fubini polynomials associated with \( Y \). The paper derives properties, explicit expressions, recurrence relations, and identities for these polynomials and numbers. Special cases of \( Y \) include the gamma random variable, the Poisson random variable, and the Bernoulli random variable. The authors provide detailed proofs and examples to illustrate the theoretical results. The article is published in *Mathematical and Computer Modelling of Dynamical Systems* and is available online.