Article ID: MTJPAM-D-23-00006

Title: Study on the degenerate higher-order new Fubini-type numbers and polynomials

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00006; Volume 6 / Issue 3 / Year 2024, Pages 16-33

Document Type: Research Paper

Author(s): ‪Hye Kyung Kim a

aDepartment of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea

Received: 7 April 2023, Accepted: 31 May 2023, Published: 10 July 2023

Corresponding Author: Hye Kyung Kim (Email address:

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In this paper, we first consider the new two-variables Fubini-type numbers and polynomials of the order r arising from the fermionic p-adic integral on \underbrace{\mathbb{Z}_p \times \cdots \times \mathbb{Z}_p}_{r-times} and those degenerate version. We derive some interesting properties and recurrence relations on those numbers and polynomials. Second, we study the degenerate new two-variables Fubini-type numbers and polynomials of order r as one of the generalizations of these new two-variables Fubini-type numbers and polynomials by using the \lambda-Sheffer sequences. When \lambda \rightarrow 0, we obtain interesting identities for those degenerate new two-variables Fubini-type numbers and polynomials of order r. Some of them include the degenerate and other special polynomials and numbers such as the degenerate Bernoulli polynomials and numbers of order s, the degenerate Euler polynomials and numbers of order s, the degenerate Frobenius-Euler polynomials of order r, the degenerate Lah-Bell polynomials, and so on.

Keywords: Stirling numbers of the second kind, Bell numbers and polynomials, p-adic fermionic integral, two-variables Fubini numbers and polynomials, \lambda-Sheffer sequences

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