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 2 , 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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