2022Applied Mathematics in Science and EngineeringOpen access

Some properties on degenerate Fubini polynomials

Taekyun Kim, Dae San Kim, Hye Kyung Kim, Hyunseok Lee

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Abstract

The nth Fubini number enumerates 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. There are many variants of Fubini numbers and polynomials. Recently, the degenerate Fubini polynomials were introduced by Kim-Kim-Jang as a degenerate version of the Fubini polynomials. The aim of this article is by using generating functions and certain differential operators to further study some identities and properties on the degenerate Fubini polynomials and the higher-order degenerate Fubini polynomials.

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What this paper is about

The nth Fubini number enumerates 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. There are many variants of Fubini numbers and polynomials. Recently, the degenerate Fubini polynomials were introduced by Kim-Kim-Jang as a degenerate version of the Fubini polynomials. The aim of this article is by using generating functions and certain differential operators to further study some identities and properties on the degenerate Fubini polynomials and the higher-order degenerate Fubini polynomials.

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Available abstract

The nth Fubini number enumerates 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. There are many variants of Fubini numbers and polynomials. Recently, the degenerate Fubini polynomials were introduced by Kim-Kim-Jang as a degenerate version of the Fubini polynomials. The aim of this article is by using generating functions and certain differential operators to further study some identities and properties on the degenerate Fubini polynomials and the higher-order degenerate Fubini polynomials.

Key concepts: Fubini's theorem, Mathematics, Degenerate energy levels, Pure mathematics, Physics, Quantum mechanics

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