2023/12/15 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1 · 1 citation
Mathematics · #11B73 #11B83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2312.09485
openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to study probabilistic versions of the degenerate Whitney numbers of the second kind and those of the degenerate Dowling polynomials, namely the probabilistic degenerate Whitney numbers of the second kind associated with Y and the probabilistic degenerate Dowling polynomials associated with Y. Here Y is a random variable whose moment generating function exists in some neighborhood of the origin. We derive some properties, explicit expressions, certain identities, recurrence relations and generating functions for those numbers and polynomials. In addition, we investigate their generalizations, namely the probabilistic degenerate r-Whitney numbers of the second kind associated with Y and the probabilistic degenerate r-Dowling polynomials associated with Y, and get similar results to the aforementioned numbers and polynomials.