标题： 退化贝尔多项式的Spivey型关系的概率推广 显示英文标题

标题： Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials

摘要： 在Spivey对贝尔数的递推关系的重要发现之后，关于贝尔数和多项式的各种推广的研究已经出现。例如，Kim和Kim为退化贝尔多项式和Dowling多项式建立了一个类似Spivey的递推关系。在本文中，我们通过推导出退化贝尔多项式和退化r-贝尔多项式的类似Spivey的递推关系的概率推广来扩展这项工作。 显示英文摘要

摘要： Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type recurrence relation specifically for degenerate Bell and Dowling polynomials. In this paper, we extend this work by deriving a probabilistic generalization of Spivey-type recurrence relations for both degenerate Bell and degenerate r-Bell polynomials.