General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 3,  2009, pp.435-450
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.3.435
Title & Authors
General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction

Abstract
On page 366 of his lost notebook [15], Ramanujan recorded a cubic continued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V ($\small{q^3}$) and also establish some explicit evaluations using the values of remarkable product of theta-function.
Keywords
cubic continued fraction;modular equation;theta-function;
Language
English
Cited by
1.
A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications, Journal of Mathematics, 2013, 2013, 1
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