Two-Variable Type 2 Poly-Fubini Polynomials

Ghulam Muhiuddin, Waseem Ahmad Khan and Ugur Duran
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Ghulam Muhiuddin: Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Ugur Duran: Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay TR-31200, Turkey

Mathematics, 2021, vol. 9, issue 3, 1-13

Abstract: In the present work, a new extension of the two-variable Fubini polynomials is introduced by means of the polyexponential function, which is called the two-variable type 2 poly-Fubini polynomials. Then, some useful relations including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoulli polynomials are derived. Also, some summation formulas and an integral representation for type 2 poly-Fubini polynomials are investigated. Moreover, two-variable unipoly-Fubini polynomials are introduced utilizing the unipoly function, and diverse properties involving integral and derivative properties are attained. Furthermore, some relationships covering the two-variable unipoly-Fubini polynomials, the Stirling numbers of the second and the first kinds, and the Daehee polynomials are acquired.

Keywords: polyexponential function; Fubini polynomials; poly-Fubini polynomials; unipoly function; Stirling numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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