Degenerate r-Bell polynomials arising from degenerate normal odering

2022/08/10 by Taekyun Kim, Kim, Taekyun, Dae San Kim +3
Mathematics · Physics and Astronomy · #11B73 #11B83 #81Q99 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT) #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2208.05465

openalex publication_date 2022/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators. In particular, we obtain two expressions for the generating function of the degenerate r-Bell polynomials in |z| , and a recurrence relation and Dobinski-like formula for the degenerate r-Bell numbers. These are derived from the degenerate normal ordering of a degenerate integral power of the number operator in terms of boson operators where the degenerate r-Stirling numbers of the second kind appear as the coefficients.

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