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

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

doi:10.3934/math.2022221

AIMS Mathematics

2022, Volume 7, Issue 3: 4004-4016. doi: 10.3934/math.2022221

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Research article Special Issues

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

1.
Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2.
Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
3.
Department of Mathematical Methods in Economy, Far Eastern Federal University, 690950 Vladivostok, Russia
4.
Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea
5.
Department Of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea

Received: 29 July 2021 Accepted: 06 December 2021 Published: 13 December 2021
MSC : 11B73, 11B83

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.
Citation: Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Hye Kyung Kim, Hyunseok Lee. A new approach to Bell and poly-Bell numbers and polynomials[J]. AIMS Mathematics, 2022, 7(3): 4004-4016. doi: 10.3934/math.2022221

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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.

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