Some identities for degenerate complete and incomplete r-Bell polynomials

Abstract

In this paper, we study degenerate complete and incomplete r-Bell polynomials. They are generalizations of the recently introduced degenerate r-Bell polynomials and degenerate analogues for the complete and incomplete r-Bell polynomials. We investigate some properties and identities for these polynomials. In particular, we give explicit formulas for the degenerate complete and incomplete r-Bell polynomials. MSC: 11B73; 11B83; 05A19Keywords: Degenerate complete r-Bell polynomials; Degenerate incomplete r-Bell polynomials; Extended degenerate complete r-Bell polynomials When x = 1, Bel (r) n (λ) = Bel (r) n (1|λ) are called the degenerate r-Bell numbers.

Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials

“…These ways of investigating special polynomials and numbers can be also applied to degenerate versions of such polynomials and numbers. Indeed, in recent years, many mathematicians have drawn their attention to studies of degenerate versions of many special polynomials and numbers by using the aforementioned means ( [9,10,14] and references therein). The incomplete and complete Bell polynomials arise in many different contexts as we stated in the Introduction.…”

New type of degenerate Daehee polynomials of the second kind

“…Another way of introducing new special functions, polynomials, and numbers is studying q-analogs of special polynomials. As has been seen in the references, Kim and his research team ( [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][19][20][21]) have…”

“…Recent investigations involving degenerate Daehee polynomials and numbers of the third kind [3], degenerate λ-q-Daehee polynomials [5], degenerate polyexponential functions and degenerate Bell polynomials [14], degenerate binomial coefficients and degenerate hypergeometric functions [15], new type degenerate Bernoulli numbers [8], degenerate Stirling polynomials of the second kind [19], degenerate poly-Bernoulli numbers and polynomials [18], degenerate Daehee polynomials of the second kind [9], new type de-generate Daehee numbers and polynomials [17], some results on degenerate Daehee and Bernoulli numbers and polynomials [20], degenerate Laplace transform and degenerate gamma function [11], some identities on type 2 degenerate Bernoulli polynomials of the second sind [10], some identities for degenerate complete and incomplete r-Bell polynomials [21] have been investigated in detail.…”

Degenerate s-Extended Complete and Incomplete Lah-Bell Polynomials

“…Recently, many mathematicians have been studying various degenerate versions of special polynomials and numbers as well as enumerative combinatorics, probability theory, number theory, etc. [7][8][9][10][11][12][13][14][15][16][17]. In [7], as an example considering the psychological burden of baseball hitters, it well expresses the starting point of degenerate special polynomials and numbers being studied by many scholars.…”