General Formulas for Explicit Evaluations of Ramanujan’s Cubic Continued Fraction
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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 (q3) and also establish some explicit evaluations using the values of remarkable product of theta-function.
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 (q3) and also establish some explicit evaluations using the values of remarkable product of theta-function.
참고문헌 (15)
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