A note on Fibonacci-type polynomials

TL;DR

This paper investigates the convergence behavior of the largest real roots of Fibonacci-type polynomials defined by a specific recurrence relation, extending previous special cases for different values of k.

Contribution

It analyzes the convergence of maximal real roots for a family of Fibonacci-type polynomials with a general recurrence, generalizing known cases for k=1 and k=2.

Findings

Convergence properties of maximal real roots are established.

Extension of previous results to a broader class of Fibonacci-type polynomials.

Insights into the behavior of roots for different k values.

Abstract

We opt to study the convergence of maximal real roots of certain Fibonacci-type polynomials given by $G_n=x^kG_{n-1}+G_{n-2}$. The special cases $k=1$ and $k=2$ are found in [4] and [7], respectively.