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Article

Some Identities Involving Fubini Polynomials

1
Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China
2
College of Mathematics and Computer, Jilin Normal University, Siping 136000, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(21), 3493; https://doi.org/10.3390/math13213493
Submission received: 14 September 2025 / Revised: 29 October 2025 / Accepted: 30 October 2025 / Published: 1 November 2025

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 Fubini polynomials; Euler numbers; identities; congruence; Sums of Products

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MDPI and ACS Style

Liu, W.; Yu, K.; Cheng, X. Some Identities Involving Fubini Polynomials. Mathematics 2025, 13, 3493. https://doi.org/10.3390/math13213493

AMA Style

Liu W, Yu K, Cheng X. Some Identities Involving Fubini Polynomials. Mathematics. 2025; 13(21):3493. https://doi.org/10.3390/math13213493

Chicago/Turabian Style

Liu, Weiming, Kuai Yu, and Xiaoliang Cheng. 2025. "Some Identities Involving Fubini Polynomials" Mathematics 13, no. 21: 3493. https://doi.org/10.3390/math13213493

APA Style

Liu, W., Yu, K., & Cheng, X. (2025). Some Identities Involving Fubini Polynomials. Mathematics, 13(21), 3493. https://doi.org/10.3390/math13213493

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