The complete evaluation of Rogers Ramanujan and other continued fractions with elliptic functions

Abstract

In this article we present evaluations of continued fractions studied by Ramanujan. More precisely we give the complete polynomial equations of Rogers-Ramanujan and other continued fractions, using tools from the elementary theory of the Elliptic functions. We see that all these fractions are roots of polynomials with coeficients depending only on the inverse elliptic nome-q and in some cases the Elliptic Integral-K. In most of simplifications of formulas we use Mathematica.

arXiv comment18 pages

References in corpus (2)

• On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions
• Integrals related with Rogers Ramanujan continued fraction and q-products

Cited by in corpus (5)

• On a General Sextic Equation Solved by the Rogers Ramanujan Continued Fraction
• On the Evaluation of the Fifth Degree Elliptic Singular Moduli
• The First Derivative of Ramanujans Cubic Continued Fraction
• Generalizations of Ramanujans Continued fractions
• On the complete solution of the general quintic using Rogers-Ramanujan continued fraction