Probabilistic degenerate poly-Bell polynomials associated with random variables

2025/03/09 by Xue, Pengxiang, Ma, Yuankui, Kim, Taekyun +2 · 3 citations
#11B73 #11B83 #60-08 #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.06616

Abstract

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable 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 is the Bernoulli random variable with probability of success p or the gamma random variable with parameters 1,1.

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• Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials
• A note on new type degenerate Srirling numbers of the first kind
• Degenerate Sheffer-type polynomials and degenerate Sheffer polynomials associated with a random variable

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