On Convolved Generalized Fibonacci and Lucas Polynomials

TL;DR

This paper introduces convolved h(x)-Fibonacci and Lucas polynomials, extending classical Fibonacci numbers, and explores their combinatorial formulas and matrix representations.

Contribution

It defines convolved h(x)-Fibonacci polynomials, provides combinatorial formulas, and links them to Hessenberg matrices, offering new mathematical insights.

Findings

Derived combinatorial formulas for h(x)-Fibonacci and Lucas polynomials

Established the matrix form of convolved h(x)-Fibonacci polynomials

Extended classical Fibonacci concepts to polynomial families

Abstract

We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the convolved h(x)-Fibonacci polynomials form a family of Hessenberg matrices.