Remarks on Bell and higher order Bell polynomials and numbers

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...

Complete Bell polynomials and new generalized identities for polynomials of higher order

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of these identities is considered and generating function for polynomials satisfying this general identity is found.