A new approach to Bell and poly-Bell numbers and polynomials

Dae San Kim, Dmitry V. Dolgy, Hye-Kyung Kim, Hyunseok Lee, Taekyun Kim

Published 2021-06-28Version 1

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. We also consider degenerate versions of those polynomials and numbers, namely degenerate Bell polynomials and numbers of the second kind and degenerate poly-Bell polynomials and numbers of the second kind, and deduce their similar results.