Original Article
Kyungpook Mathematical Journal 2009; 49(3): 435-450
Published online September 23, 2009
Copyright © Kyungpook Mathematical Journal.
General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction
Megadahalli Sidda Naika Mahadeva Naika1, Mugur Chinna Swamy Maheshkumar2, Kurady Sushan Bairy3
1Department of Mathematics, Bangalore University, Central College Campus, Bangalore-560 001, INDIA
2Department of Mathematics, Bangalore University, Central College Campus, Bangalore 560 001, INDIA
3Department of Mathematics, Bangalore University, Central College Campus, Bangalore 560 001, India
On page 366 of his lost notebook cite{SR2}, 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 $V(q^3)$ and also establish some explicit evaluations using the values of remarkable product of theta-function.
Keywords: cubic continued fraction, modular equation, theta-function