Algebraic Equations Solved with Jacobi Elliptic Functions

TL;DR

This paper presents a method to solve a specific class of two-parameter polynomial-quintic equations using Jacobian elliptic functions, linking the solutions to the elliptic singular modulus.

Contribution

It introduces a novel approach connecting polynomial-quintic equations with Jacobian elliptic functions and the elliptic singular modulus.

Findings

Solution expressed in terms of elliptic singular modulus k

Method applicable to a specific class of polynomial-quintic equations

Provides explicit relation between coefficients and elliptic functions

Abstract

In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic singular modulus $k$.