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arXiv · 2208.05465

Degenerate r-Bell polynomials arising from degenerate normal odering

Taekyun Kim·Dae san Kim·Hye Kyung Kim
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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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Taekyun Kim, Dae san Kim, Hye Kyung Kim. 2022-08-10. Degenerate r-Bell polynomials arising from degenerate normal odering. https://arxiv.org/abs/2208.05465

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