The class of Lucas-Lehmer polynomials

TL;DR

This paper introduces a new sequence of polynomials inspired by the Lucas-Lehmer sequence, exploring their properties and connections to Chebyshev polynomials, expanding understanding of polynomial sequences and their recursive structures.

Contribution

The paper presents a novel polynomial sequence following Lucas-Lehmer's recursive rule and establishes its properties and relationships with Chebyshev polynomials.

Findings

The new polynomial sequence shares properties with Lucas-Lehmer and Chebyshev polynomials.

Connections between the sequence and Chebyshev polynomials are established.

Key properties of the sequence are characterized and analyzed.

Abstract

In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the first and second kind.