On the complete solution of the general quintic using Rogers-Ramanujan continued fraction

TL;DR

This paper presents a novel method to solve the general quintic equation explicitly using the Rogers-Ramanujan continued fraction, expressing roots as algebraic functions of this continued fraction.

Contribution

It introduces a new approach linking the Rogers-Ramanujan continued fraction to the explicit solution of the general quintic equation.

Findings

Root of the quintic expressed as algebraic function of Rogers-Ramanujan continued fraction

Provides explicit formula for solving the general quintic

Connects continued fractions with algebraic solutions of polynomial equations

Abstract

In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction.