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Research Article | Open Access

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

Taekyun Kim1( ), Dae San Kim2, Dmitry V. Dolgy3,4, Hye Kyung Kim5( ), Hyunseok Lee1
Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Department of Mathematical Methods in Economy, Far Eastern Federal University, 690950 Vladivostok, Russia
Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea
Department Of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea
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Abstract

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.

Keywords

Bell polynomials of the second kinddegenerate Bell polynomials of the second kindpoly-Bell polynomials of the second kinddegenerate poly-Bell polynomials of the second kind
CLC number: 11B73, 11B83

References

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4004-4016
DOI: 10.3934/math.2022221

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Cite this article:
Kim T, Kim DS, Dolgy DV, et al. A new approach to Bell and poly-Bell numbers and polynomials. AIMS Mathematics, 2022, 7(3): 4004-4016. https://doi.org/10.3934/math.2022221

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Received: 29 July 2021
Accepted: 06 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)