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arXiv · 2503.06616

Probabilistic degenerate poly-Bell polynomials associated with random variables

Pengxiang Xue·Yuankui Ma·Taekyun Kim·Dae San Kim·Wenpeng Zhang
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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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Pengxiang Xue, Yuankui Ma, Taekyun Kim, Dae San Kim, Wenpeng Zhang. 2025-03-09. Probabilistic degenerate poly-Bell polynomials associated with random variables. https://arxiv.org/abs/2503.06616

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