Axioms (Apr 2025)

Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers

  • Waleed Mohamed Abd-Elhameed,
  • Omar Mazen Alqubori,
  • Abdulrahim A. Alluhaybi,
  • Amr Kamel Amin

DOI
https://doi.org/10.3390/axioms14040286
Journal volume & issue
Vol. 14, no. 4
p. 286

Abstract

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This article introduces new polynomials that extend the standard Leonardo numbers, generalizing Fibonacci and Lucas polynomials. A new power form representation is developed for these polynomials, which is crucial for deriving further formulas. This article also presents two connection formulas linking these generalized polynomials to the Fibonacci and Lucas polynomials, as well as several identities involving some generalized and specific Leonardo numbers. Additionally, new product formulas involving the generalized Leonardo polynomials with the Fibonacci and Lucas polynomials are provided, along with computations of definite integrals based on the derived formulas.

Keywords