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Investigating the Properties and Dynamic Applications of Δ h Legendre–Appell Polynomials

Author

Listed:
  • Noor Alam

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Shahid Ahmad Wani

    (Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Pune 412115, Maharashtra, India)

  • Waseem Ahmad Khan

    (Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia)

  • Hasan Nihal Zaidi

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

Abstract

This research aims to introduce and examine a new type of polynomial called the Δ h Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δ h Legendre–Appell polynomials and explore their properties. We derive the generating function and recurrence relations for these polynomials and their explicit formulas, recurrence relations, and summation formulas. We also verify the monomiality principle for these polynomials and express them in determinant form. Additionally, we establish similar results for the Δ h Legendre–Bernoulli, Euler, and Genocchi polynomials.

Suggested Citation

  • Noor Alam & Shahid Ahmad Wani & Waseem Ahmad Khan & Hasan Nihal Zaidi, 2024. "Investigating the Properties and Dynamic Applications of Δ h Legendre–Appell Polynomials," Mathematics, MDPI, vol. 12(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1973-:d:1422369
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    References listed on IDEAS

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    1. Juan Hernández & Dionisio Peralta & Yamilet Quintana, 2023. "A Look at Generalized Degenerate Bernoulli and Euler Matrices," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
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