On bivariate Apostol-Fubini polynomials of higher order

Volume 23, Issue 1, pp 10--25 http://dx.doi.org/10.22436/jmcs.023.01.02

Publication Date: October 02, 2020 Submission Date: July 29, 2020 Revision Date: August 12, 2020 Accteptance Date: August 17, 2020

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Authors

Nestor G. Acala - Mathematics Department, Main Campus, Mindanao State University, Marawi City, Lanao Del Sur 9700, Philippines.

Abstract

Recently, some generalizations of the Apostol-Bernoulli polynomials, Apostol-Euler polynomials, and Apostol-Genocchi polynomials were introduced (see for instance [V. Kurt, Appl. Math. Sci., \(\bf 3\) (2009), 2757--2764], [Q.-M. Luo, Taiwanese J. Math., \(\bf 10\) (2006), 917--925], [Q.-M. Luo, H. M. Srivastava, J. Math. Anal. Appl., \(\bf 308\) (2005), 290--302], [D. Q. Lu, H. M. Srivastava, Comput. Math. Appl., \(\bf 62\) (2011), 3591--3602] and [W. Wang, C. Jia, T. Wang, Comput. Math. Appl., \(\bf 55\) (2008), 1322--1332]). In this paper, we introduce and investigate an analogous generalization of Fubini polynomials of higher order, which we call bivariate Apostol-Fubini polynomials of higher order. We then obtain an explicit formula of these generalized Fubini polynomials and establish several symmetry identities. Moreover, we also establish relations of these polynomials with other Apostol-type numbers and polynomials.

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Keywords

• Fubini numbers
• Fubini polynomials
• generalized Fubini polynomials of higher order
• Apostol-Bernoulli polynomials
• Apostol-type polynomials
• \(\lambda\)-Stirling numbers of the second kind
• Gauss hypergeometric functions

MSC

•  11B68
•  11B73
•  05A10
•  11B65
•  33C05
•  11B83

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