On poly-Bell numbers and polynomials

Bell polynomials and Fibonacci numbers

On degenerate numbers and polynomials related to the Stirling numbers and the Bell polynomials

In this paper, we consider the degenerate numbers Rn(λ) and polynomials Rn(x, λ) related to the Stirling numbers and the Bell polynomials. We also obtain some explicit formulas for degenerate numbers Rn(λ) and polynomials Rn(x, λ). AMS subject classification: 11B68, 11S40, 11S80.

A Linear Binomial Recurrence and the Bell Numbers and Polynomials

By iterating (0.2), f(n + r) can be written as a linear combination of binomial coefficients with polynomial coefficients Arj(n), 0 ≤ j ≤ r − 1. The polynomials Arj(n) have various interesting properties. This paper provides a sampling of these properties, including two new ways to represent B(n) in terms of Arj (n).

Generalizations of the Bell Numbers and Polynomials and Their Properties

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers o...

A Note on Degenerate Hermite Poly–bernoulli Numbers and Polynomials

In this paper, we introduce a new class of degenerate Hermite poly-Bernoulli polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of d...