Some identities involving derangement polynomials and $ r $-Bell polynomials

Aimin Xu; Aimin Xu

doi:10.3934/math.2024102

AIMS Mathematics

2024, Volume 9, Issue 1: 2051-2062. doi: 10.3934/math.2024102

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Research article

Some identities involving derangement polynomials and $ r $-Bell polynomials

Aimin Xu ^,

Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China

Received: 29 September 2023 Revised: 28 November 2023 Accepted: 12 December 2023 Published: 20 December 2023
MSC : 05A10, 05A19, 11B83

In this paper two kinds of identities involving derangement polynomials and $ r $-Bell polynomials were established. The identities of the first kind extended the identity on derangement numbers and Bell numbers due to Clarke and Sved and its generalizations due to Du and Fonseca. The identities of the second kind extended some of the results on derangement polynomials and Bell polynomials due to Kim et al.
- derangement polynomials,
- $ r $-Bell polynomials,
- Stirling numbers,
- identities
Citation: Aimin Xu. Some identities involving derangement polynomials and $ r $-Bell polynomials[J]. AIMS Mathematics, 2024, 9(1): 2051-2062. doi: 10.3934/math.2024102

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Abstract

In this paper two kinds of identities involving derangement polynomials and $ r $-Bell polynomials were established. The identities of the first kind extended the identity on derangement numbers and Bell numbers due to Clarke and Sved and its generalizations due to Du and Fonseca. The identities of the second kind extended some of the results on derangement polynomials and Bell polynomials due to Kim et al.

References

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