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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yasir A. Madani & Abdulghani Muhyi & Khaled Aldwoah & Amel Touati & Khidir Shaib Mohamed & Ria H. Egami, 2025. "Construction of a Hybrid Class of Special Polynomials: Fubini–Bell-Based Appell Polynomials and Their Properties," Mathematics, MDPI, vol. 13(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:1009-:d:1616585
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