Two variable higher-order Fubini polynomials

Dae San Kim; Taekyun Kim; Hyuck-In Kwon; Jin-Woo Park

doi:10.4134/JKMS.j170573

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2018; 55(4): 975-986

Online first article December 6, 2017 Printed July 1, 2018

https://doi.org/10.4134/JKMS.j170573

Two variable higher-order Fubini polynomials

Dae San Kim, Taekyun Kim, Hyuck-In Kwon, Jin-Woo Park

Sogang University, Kwangwoon University, Kwangwoon University, Daegu University

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Abstract

Some new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomilas were introduced recently by Kilar and Simsek (\cite{5}) and we study the two variable Fubini polynomials as Appell polynomials whose coefficients are the Fubini polynomials. In this paper, we would like to utilize umbral calculus in order to study two variable higher-order Fubini polynomials. We derive some of their properties, explicit expressions and recurrence relations. In addition, we express the two variable higher-order Fubini polynomials in terms of some families of special polynomials and vice versa.

Keywords: umbral calculus, two variable higher-order Fubini polynomials

MSC numbers: 11B68, 11B83, 42A16