Construction of a Hybrid Class of Special Polynomials: Fubini–Bell-Based Appell Polynomials and Their Properties

Yasir A. Madani, Abdulghani Muhyi, Khaled Aldwoah (), Amel Touati, Khidir Shaib Mohamed () and Ria H. Egami
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Yasir A. Madani: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Abdulghani Muhyi: Department of Mechatronics Engineering, Faculty of Engineering and Smart Computing, Modern Specialized University, Sana’a, Yemen
Khaled Aldwoah: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia
Amel Touati: Department of Mathematics, Faculty of Science, Northern Border University, Arar 73213, Saudi Arabia
Khidir Shaib Mohamed: Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
Ria H. Egami: Department of Mathematics, College of Science and Humanity, Prince Sattam bin Abdulaziz University, Sulail, Al-Kharj 11942, Saudi Arabia

Mathematics, 2025, vol. 13, issue 6, 1-21

Abstract: This paper aims to establish a new hybrid class of special polynomials, namely, the Fubini–Bell-based Appell polynomials. The monomiality principle is used to derive the generating function for these polynomials. Several related identities and properties, including symmetry identities, are explored. The determinant representation of the Fubini–Bell-based Appell polynomials is also established. Furthermore, some special members of the Fubini–Bell-based Appell family—such as the Fubini–Bell-based Bernoulli polynomials and the Fubini–Bell-based Euler polynomials—are derived, with analogous results presented for each. Finally, computational results and graphical representations of the zero distributions of these members are investigated.

Keywords: Fubini polynomials; Bell polynomials; Appell polynomials; monomiality principle; generating function; determinant representation; differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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