On a General Sextic Equation Solved by the Rogers Ramanujan Continued Fraction

Abstract

In this article we solve a general class of sextic equations. The solution follows if we consider the $j$-invariant and relate it with the polynomial equation's coefficients. The form of the solution is a relation of Rogers-Ramanujan continued fraction. The inverse technique can also be used for the evaluation of the Rogers-Ramanujan continued fraction, in which the equation is not now the depressed equation but another quite more simplified equation.

23 pages, Rogers Ramanujan Continued Fraction, Sextic Equation

References in corpus (6)

• Properties of Quantum Graphity at Low Temperature
• The complete evaluation of Rogers Ramanujan and other continued fractions with elliptic functions
• Solutions by radicals at singular values k_N from new class invariants for N \equiv 3 mod 8
• Integrals related with Rogers Ramanujan continued fraction and q-products
• On the Evaluation of the Fifth Degree Elliptic Singular Moduli
• Jacobian Elliptic Functions, Continued Fractions and Ramanujan Quantities

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• On the Complete Evaluation of Jacobi Theta Functions
• Solution of Polynomial Equations with Nested Radicals
• Generalized Elliptic Integrals and Applications
• On Algebraic Functions