Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering

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 th...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
Main Authors: Kim, Taekyun, Kim, Dae San, Kim, Hye Kyung
Format: Article
Language:English
Subjects:
Bells
Combinatorial analysis
Mathematics
Operators (mathematics)
Physics
Polynomials
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Summary: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 z2, 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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/2626249