Some Identities Involving Fubini Polynomials

Weiming Liu, Kuai Yu and Xiaoliang Cheng ()
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Weiming Liu: Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China
Kuai Yu: College of Mathematics and Computer, Jilin Normal University, Siping 136000, China
Xiaoliang Cheng: College of Mathematics and Computer, Jilin Normal University, Siping 136000, China

Mathematics, 2025, vol. 13, issue 21, 1-18

Abstract: Using Hoppe’s formula, we derive two identities that relate the powers and derivatives of the generating function for Fubini polynomials. As applications, we obtain several identities involving Fubini polynomials, including identities for Sums of Products of Fubini polynomials. These results refine and extend those established in two previous papers by other authors. Furthermore, we prove conjectures posed in one of these papers and derive several congruence identities for Fubini numbers.

Keywords: Fubini polynomials; Euler numbers; identities; congruence; Sums of Products (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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