Explicit evaluations of a level 13 analogue of the Rogers-Ramanujan continued fraction

DOI10.1016/j.jnt.2013.12.015zbMath1294.11118OpenAlexW2022585325MaRDI QIDQ2017206

Dongxi Ye, Shaun Cooper

Publication date: 25 June 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.12.015

zbMATH Keywords

Rogers-Ramanujan continued fractionreciprocity formulaKronecker limit formulaRamanujan-Weber class invariant\(P-Q\) modular equation

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Continued fractions and generalizations (11J70) Holomorphic modular forms of integral weight (11F11) Elliptic functions and integrals (33E05)

Related Items

The level 13 analogue of the Rogers-Ramanujan continued fraction and its modularity, Properties of reciprocity formulas for the Rogers-Ramanujan continued fractions, Level 17 Ramanujan-Sato series, Explicit evaluations of a level 13 analogue of the Rogers-Ramanujan continued fraction, Hypergeometric transformation formulas of degrees 3, 7, 11 and 23, Ramanujan's function \(k(\tau)=r(\tau)r^2(2\tau)\) and its modularity, New general theorems and explicit values of the level 13 analogue of Rogers-Ramanujan continued fraction, The Rogers-Ramanujan continued fraction and its level 13 analogue

Cites Work

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• Theta function identities
• On the Rogers-Ramanujan continued fraction
• Ramanujan's continued fraction
• New Ramanujan-Kolberg type partition identities.
• Certain modular functions similar to the Dedekind eta function.
• Explicit evaluations of a level 13 analogue of the Rogers-Ramanujan continued fraction
• Evaluations of the Rogers–Ramanujan continued fraction R(q) by modular equations
• On Ramanujan's continued fraction
• Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations
• Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)
• Continued fractions and modular functions
• Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
• Ramanujan's explicit values for the classical theta‐function
• Some Values for the Rogers-Ramanujan Continued Fraction
• Ramanujan's class invariants and cubic continued fraction