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

Degenerate r-Bell polynomials arising from degenerate normal odering