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

Naika, Megadahalli Sidda Naika Mahadeva; Maheshkumar, Mugur Chinna Swamy; Bairy, Kurady Sushan;

Naika, Megadahalli Sidda Naika Mahadeva; Maheshkumar, Mugur Chinna Swamy; Bairy, Kurady Sushan;

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 () 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.

CERTAIN IDENTITIES FOR A CONTINUED FRACTION OF RAMANUJAN,;;;

Advanced Studies in Contemporary Mathematics, 2014. vol.24. 1, pp.45-66

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