Chebyshev Polynomials and the Minimal Polynomial of cos(2π/ n )

2017/01/01 by Yusuf Z. Gürtaş · 2 citations
Mathematics · #Mathematical functions and polynomials #Advanced Mathematical Identities #Fractional Differential Equations Solutions #Chebyshev polynomials #Mathematics #Polynomial #Chebyshev nodes #Combinatorics #Classical orthogonal polynomials #Orthogonal polynomials #Discrete mathematics #Mathematical analysis

paper · doi:10.4169/amer.math.monthly.124.1.74

openalex publication_date 2017/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/02/01

Abstract

The minimal polynomial of cos(2π/n) allows one to realize the value of cos(2π/n) as the root of a polynomial with rational coefficients. These polynomials prove to be instrumental in expressing some relations satisfied by Chebyshev polynomials as a product. In this article a few relations satisfied by Chebyshev polynomials of the first and second kind and the minimal polynomial of cos(2π/n) are presented. The proof of the main theorem shows how cyclotomic polynomials can be used to link these two kinds of polynomials.

Cited by

• Factoring Variants of Chebyshev Polynomials of the First and Second Kinds with Minimal Polynomials of cos(2π/d)
• Chebyshev polynomials [wikipedia]