Abstract
In this paper, we introduce the extended degenerate r-central factorial numbers of the second kind and the extended degenerate r-central Bell polynomials. They are extended versions of the degenerate central factorial numbers of the second kind and the degenerate central Bell polynomials, and also degenerate versions of the extended r-central factorial numbers of the second kind and the extended r-central Bell polynomials, all of which have been studied by Kim and Kim. We study various properties and identities concerning those numbers and polynomials and also their connections.
Highlights
For λ ∈ R, we recall that the degenerate exponential function eλx (t) is defined by
In Reference [3], the degenerate central factorial polynomials of the second kind are defined by k!
Let us recall that the degenerate central Bell polynomials are defined by
Summary
One can show that the generating function of central factorial x [n] , (n ≥ 0), is given by (see [3,15,16,17,18,19,20]) As is defined in [18], for any non-negative integer n, the central factorial numbers of the first kind are given by x [n] = In Reference [22] were introduced the central Bell polynomials defined by e t
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