Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials

TL;DR

This paper extends Spivey's recurrence relation to degenerate Bell and r-Bell polynomials using a probabilistic approach, enriching the theoretical framework of these special polynomials.

Contribution

It introduces a novel probabilistic generalization of Spivey-type recurrence relations for degenerate Bell and degenerate r-Bell polynomials.

Findings

Derived a probabilistic recurrence relation for degenerate Bell polynomials.

Extended the recurrence relation to degenerate r-Bell polynomials.

Provides a new theoretical tool for studying degenerate Bell polynomials.

Abstract

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.