A Class of Periodic Continued Radicals

TL;DR

This paper investigates the limits of a specific class of periodic continued radicals and reveals their relationship with the fixed points of Chebyshev polynomials, providing new insights into their mathematical properties.

Contribution

It introduces a novel connection between periodic continued radicals and Chebyshev polynomial fixed points, expanding understanding of their mathematical structure.

Findings

Computed limits of the class of periodic continued radicals.

Established a link between these radicals and Chebyshev polynomial fixed points.

Provided new theoretical insights into the properties of these radicals.

Abstract

We compute the limits of a class of periodic continued radicals and we establish a connection between them and the fixed points of the Chebycheff polynomials.