April 2, 2024Open Access

Generalization of Spivey's recurrence relation

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Abstract

In 2008, Spivey found a recurrence relation for the Bell numbers. We consider the probabilistic r-Bell polynomials associated with which are a probabilistic extension of the r-Bell polynomials. Here Y is a random variable whose moment generating function exists in some neighborhood of the origin . The aim of this paper is to generalize the relation for the Bell numbers to that for the probabilistic r-Bell polynomials associated with Y.

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Kim et al. (Tue,) studied this question.

synapsesocial.com/papers/68e70d86b6db643587686892 https://doi.org/https://doi.org/10.48550/arxiv.2404.02413

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