Degenerate r-Whitney numbers and degenerate r-Dowling polynomials via boson operators

Poisson degenerate central moments related to degenerate Dowling and degenerate r-Dowling polynomials

“…In recent years, studying various degenerate versions of many special polynomials and numbers, which began with the paper [4] by Carlitz, received regained interests of some mathematicians and many interesting results were discovered (see [12][13][14][15][16][17][18] and the references therein). They have been explored by employing several different tools such as combinatorial methods, generating functions, p-adic analysis, umbral calculus techniques, differential equations, probability theory and analytic number theory.…”

Degenerate Lah–Bell polynomials arising from degenerate Sheffer sequences

“…It turns out that it is fascinating and fruitful to study varioius degenerate versions of some special polynomials and numbers (see [6][7][8][9][10][11][12] and the references therein), which has its origin in the work of Carlitz in [2]. They have been explored by using various different methods and led to the introduction of degenerate gamma functions and degenerate umbral calculus.…”

“…(see [2,[6][7][8][9]12]). (2) For r ∈ Z with r ≥ 0, the degenerate r-Stirling numbers of the second kind are defined by Kim-Kim as…”

“…The number operator is defined by n|k = k|k , (k ≥ 0), (see [5,8,9]). ( 9) By ( 8) and ( 9), we get n = a † a.…”

“…, (see [1,5,8,13]), (10) where S 2 (k, l) are the Stirling numbers of the second kind defined by x n = ∑ n k=0 S 2 (n, k)(x) k , (see [3,14]).…”