A note on (<em>p</em>, <em>q</em>)-analogue type of Fubini numbers and polynomials

Waseem Ahmad Khan; Kottakkaran Sooppy Nisar; Dumitru Baleanu; Waseem Ahmad Khan; Kottakkaran Sooppy Nisar; Dumitru Baleanu

doi:10.3934/math.2020177

AIMS Mathematics

2020, Volume 5, Issue 3: 2743-2757. doi: 10.3934/math.2020177

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Research article

A note on (p, q)-analogue type of Fubini numbers and polynomials

1.
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P. O. Box 1664, Al Khobar 31952, Kingdom of Saudi Arabia
2.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
3.
Department of Mathematics, Cankaya University, Turkey
4.
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan

Received: 29 September 2019 Accepted: 09 March 2020 Published: 17 March 2020
MSC : 11B68, 11B73, 11B75, 11B83, 05A30

In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.
Citation: Waseem Ahmad Khan, Kottakkaran Sooppy Nisar, Dumitru Baleanu. A note on (p, q)-analogue type of Fubini numbers and polynomials[J]. AIMS Mathematics, 2020, 5(3): 2743-2757. doi: 10.3934/math.2020177

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Abstract

In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.

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