Variations on Ramanujan's nested radicals

TL;DR

This paper introduces new nested radical equations inspired by Ramanujan's work, explores various methods of constructing such radicals, and highlights the lack of a comprehensive theory for these intriguing mathematical expressions.

Contribution

It presents novel nested radical equations similar to Ramanujan's and discusses multiple methods for constructing these radicals, addressing gaps in existing theoretical understanding.

Findings

New nested radical equations similar to Ramanujan's

Multiple methods for constructing nested radicals

No comprehensive theory currently explains these results

Abstract

We give new nested radical equations of similar kind to Ramanujan's questions to the Indian Mathematical Society 100 years ago. While many have since considered these from the perspectives of the Notebooks of Ramanujan and from the theory of Class numbers and Units, there seems no comprehensive theory to cover off the results, and it seems always possible to find new and surprizing elementary equations of this kind. We also consider a few more methods of constructing nested radicals.