On Bell Numbers and Polynomials

Abstract

The Bell polynomials is widely used in many problems in physics and mathematics. The objective of this work is to study a class of generalizations of Bell numbers and polynomials, known as poly-Bell numbers and polynomials. In the first chapter, we introduce the basic concepts necessary for the development of the second chapter. The latter presents the class of Bell numbers and polynomials, along with their generalization. We define these concepts and discuss some fundamental properties such as generating functions, explicit expressions, recurrence relations, and certain identities involving these numbers and polynomials