Open AccessA new approach to Bell and poly-Bell numbers and polynomials
Author(s) -
Taekyun Kim,
AUTHOR_ID,
Дае Сан Ким,
Dmitry V. Dolgy,
Hye Kyung Kim,
Hyunseok Lee,
AUTHOR_ID,
AUTHOR_ID,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022221
Subject(s) - bell polynomials , mathematics , difference polynomials , wilson polynomials , hahn polynomials , orthogonal polynomials , discrete orthogonal polynomials , classical orthogonal polynomials , macdonald polynomials , koornwinder polynomials , degenerate energy levels , combinatorics , discrete mathematics , pure mathematics , gegenbauer polynomials , algebra over a field , physics , quantum mechanics
Bell polynomials are widely applied in many problems arising from physics and engineering. The aim of this paper is to introduce new types of special polynomials and numbers, namely 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.