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.

In this paper, authors found a new and interesting identity between Changhee polynomials and some degenerate polynomials such as degenerate Bernoulli polynomials of the first and second kind, degenerate Euler polynomials, degenerate Daehee polynomials, degenerate Bell polynomials, degenerate Lah–Bell polynomials, and degenerate Frobenius–Euler polynomials and Mittag–Leffer polynomials by using λ -Sheffer sequences and λ -differential operators to find the coefficient polynomial when expressing the n -th Changhee polynomials as a linear combination of those degenerate polynomials. In addition, authors derive the inversion formulas of these identities.

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