On degenerate generalized Fubini polynomials

Taekyun Kim; Dae San Kim; Hyunseok Lee; Jonkyum Kwon; Taekyun Kim; Dae San Kim; Hyunseok Lee; Jonkyum Kwon

doi:10.3934/math.2022679

AIMS Mathematics

2022, Volume 7, Issue 7: 12227-12240. doi: 10.3934/math.2022679

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Research article

On degenerate generalized Fubini 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 Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea

Received: 12 March 2022 Revised: 14 April 2022 Accepted: 15 April 2022 Published: 24 April 2022
MSC : 11B73, 11B83, 65C50

The $ n $-th Fubini number counts the number of ordered partitions of a set with $ n $ elements and is the number of possible ways to write the Fubini formula for a summation of integration of order $ n $. Further, Fubini polynomials are natural extensions of the Fubini numbers. Recently, the generalized Fubini polynomials were introduced by Sebaoui-Laissaoui-Guettai-Rahmani, as one of the variants of the Fubini polynomials. The aim of this paper is to study the degenerate generalized Fubini polynomials, which are a degenerate version of those polynomials, and to find an application of them to probability theory in connection with geometric random variable.
Citation: Taekyun Kim, Dae San Kim, Hyunseok Lee, Jonkyum Kwon. On degenerate generalized Fubini polynomials[J]. AIMS Mathematics, 2022, 7(7): 12227-12240. doi: 10.3934/math.2022679

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Abstract

The $ n $-th Fubini number counts the number of ordered partitions of a set with $ n $ elements and is the number of possible ways to write the Fubini formula for a summation of integration of order $ n $. Further, Fubini polynomials are natural extensions of the Fubini numbers. Recently, the generalized Fubini polynomials were introduced by Sebaoui-Laissaoui-Guettai-Rahmani, as one of the variants of the Fubini polynomials. The aim of this paper is to study the degenerate generalized Fubini polynomials, which are a degenerate version of those polynomials, and to find an application of them to probability theory in connection with geometric random variable.

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