New expressions for certain polynomials combining Fibonacci and Lucas polynomials

被引：0
作者：
Abd-Elhameed, Waleed Mohamed [1 ]
Alqubori, Omar Mazen [2 ]
机构：
[1] Cairo Univ, Fac Sci, Dept Math, Giza 12613, Egypt
[2] Univ Jeddah, Coll Sci, Dept Math & Stat, Jeddah, Saudi Arabia
来源：
AIMS MATHEMATICS | 2025年 / 10卷 / 02期
关键词：
Fibonacci and Lucas polynomials; orthogonal polynomials; recursive formulas; moment formulas; generalized hypergeometric functions; definite integrals; LINEARIZATION FORMULAS; GENERALIZED FIBONACCI; IDENTITIES; CONNECTION; SEQUENCES;
D O I：
10.3934/math.2025136
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a new sequence of polynomials that combines the Fibonacci and Lucas polynomials. We will refer to these polynomials as merged Fibonacci-Lucas polynomials (MFLPs). We will show that we can represent these polynomials by combining two certain Fibonacci polynomials. This formula will be essential for determining the power form representation of these polynomials. This representation and its inversion formula for these polynomials are crucial to derive new formulas about the MFLPs. New derivative expressions for these polynomials are given as combinations of several symmetric and non-symmetric polynomials. We also provide the inverse formulas for these formulas. Some new product formulas involving the MFLPs have also been derived. We also provide some definite integral formulas that apply to the derived formulas.
引用
收藏
页码：2930 / 2957
页数：28
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