Parametric Evaluations of the Rogers Ramanujan Continued Fraction
Nikos Bagis
TL;DR
This paper uses inverse singular moduli functions to evaluate the Rogers-Ramanujan continued fraction and its derivative, providing new insights into their properties and evaluations.
Contribution
It introduces a novel method leveraging inverse singular moduli to evaluate the Rogers-Ramanujan continued fraction and its derivative.
Findings
Explicit evaluations of the Rogers-Ramanujan continued fraction
Derivatives of the continued fraction evaluated explicitly
New relationships between singular moduli and continued fractions
Abstract
In this article with the help of the inverse function of the singular moduli we evaluate the Rogers Ranmanujan continued fraction and his first derivative.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical functions and polynomials