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General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction
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  • 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;
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 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
1.
A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications, Journal of Mathematics, 2013, 2013, 1  crossref(new windwow)
2.
Formulas for cubic partition with 3-cores, Journal of Mathematical Analysis and Applications, 2017, 453, 1, 20  crossref(new windwow)
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