Extended Degenerate r-Central Factorial Numbers of the Second Kind and Extended Degenerate r-Central Bell Polynomials

Abstract

In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials associated with them. As results, we give some expressions, identities and properties about the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials. 2010 Mathematics Subject Classification. 11B73; 11B83; 05A19. Key words and phrases. extended degenerate Stirling numbers of the second kind, extended degenerate Bell polynomials.

Unified Degenerate Central Bell Polynomials

“…Kim et al [16] considered partially degenerate Bell polynomials numbers and developed their properties and identities. Kim et al [17] de…ned and studied on the extended degenerate r-central factorial numbers of the second kind and the extended degenerate rcentral Bell polynomials. Kwon et al [18] considered degenerate Changhee polynomials and proved several relations and formulas for these polynomials.…”

Some identities for degenerate complete and incomplete r-Bell polynomials

“…In particular, we will give some explicit formulas for the degenerate complete and incomplete r-Bell polynomials. Lastly, we mention that the extended degenerate r-central factorial numbers of the second kind and extended degenerate r-central Bell polynomials have been treated in [15].…”

A Note on Some Identities of New Type Degenerate Bell Polynomials

“…Studies on degenerate versions of some special polynomials can be traced back at least as early as the paper by Carlitz [1] on degenerate Bernoulli and degenerate Euler polynomials and numbers. In recent years, many mathematicians have drawn their attention in investigating various degenerate versions of quite a few special polynomials and numbers and discovered some interesting results on them [2][3][4][5][6][7][8][9]. This idea of introducing various degenerate versions of some special polynomials and numbers has been not only applied to polynomials but also extended to transcendental functions, so that for example, the degenerate gamma functions were introduced in [10,11].…”

“…When x = 1, B n = B n (1) are called Bell numbers. For λ ∈ R, the degenerate exponential function e x λ (t) is defined as (see [1,2,[4][5][6][7]10,11])…”