Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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General Formulas for Explicit Evaluations of Ramanujan's Cubic Continued Fraction

  • Received : 2008.02.16
  • Accepted : 2008.07.08
  • Published : 2009.09.30
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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 ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.

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References

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