**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}

^{a}Department 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: hkkim@cu.ac.kr)

**Full Text:** PDF

**Abstract**

In this paper, we first consider the new two-variables Fubini-type numbers and polynomials of the order arising from the fermionic -adic integral on 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 as one of the generalizations of these new two-variables Fubini-type numbers and polynomials by using the -Sheffer sequences. When , we obtain interesting identities for those degenerate new two-variables Fubini-type numbers and polynomials of order . Some of them include the degenerate and other special polynomials and numbers such as the degenerate Bernoulli polynomials and numbers of order , the degenerate Euler polynomials and numbers of order , the degenerate Frobenius-Euler polynomials of order , the degenerate Lah-Bell polynomials, and so on.

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

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