A Class of Continued Radicals

TL;DR

This paper investigates the limits of a broad class of continued radicals, extending prior work that focused solely on periodic cases, thereby generalizing the understanding of their convergence behavior.

Contribution

It introduces a comprehensive analysis of continued radicals beyond periodic cases, providing new methods to compute their limits.

Findings

Derived explicit formulas for limits of non-periodic continued radicals

Extended previous results to a wider class of radicals

Provided convergence criteria for the studied radicals

Abstract

We compute the limits of a class of continued radicals extending the results of a previous note in which only periodic radicals of the class were considered.