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

  • Naika, Megadahalli Sidda Naika Mahadeva (Department of Mathematics, Bangalore University, Central College Campus) ;
  • Maheshkumar, Mugur Chinna Swamy (Department of Mathematics, Bangalore University, Central College Campus) ;
  • Bairy, Kurady Sushan (Department of Mathematics, Bangalore University, Central College Campus)
  • Received : 2008.02.16
  • Accepted : 2008.07.08
  • Published : 2009.09.30

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 ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.

Keywords

cubic continued fraction;modular equation;theta-function

References

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Cited by

  1. A Product of Theta-Functions Analogous to Ramanujan's Remarkable Product of Theta-Functions and Applications vol.2013, 2013, https://doi.org/10.1155/2013/620756
  2. Formulas for cubic partition with 3-cores vol.453, pp.1, 2017, https://doi.org/10.1016/j.jmaa.2017.03.078