Abstract
In this paper, we consider of generalized central complete and incomplete Bell polynomials called degenerate central complete and incomplete Bell polynomials. These polynomials are generalizations of the recently introduced central complete Bell polynomials and `degenerate' analogues for the central complete and incomplete Bell polynomials. We investigate some properties and identities for these polynomials. Especially, we give explicit formulas for the degenerate central complete and incomplete Bell polynomials related to degenerate central factorial numbers of the second kind.
Highlights
Introduction and preliminariesThe Stirling numbers of the second kind are given by (1) 1k = k! ∞ tn S2(n, k) n!,(see [4, 5, 7, 8, 13, 14]). n=k2010 Mathematics Subject Classification
It is well known that the Bell polynomials are defined by ex(et−1) =
It is known that the central factorial numbers of the second kind are given by
Summary
It is known that the central factorial numbers of the second kind are given by In [12], the central Bell polynomials Bn(c)(x) are defined by n For λ ∈ R, we define the degenerate exponential function as follows: (13) When x = 1, Bn,λ = Bn,λ(1) are called the degenerate Bell numbers. M=1 n=k where k is a non-negative integer and (x)m,λ is the degenerate falling factorial sequence given by
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