Two modular equations for squares of the Rogers-Ramanujan functions with applications

DOI10.1007/s11139-008-9121-5zbMath1193.33230OpenAlexW1987728688MaRDI QIDQ987530

Chadwick Gugg

Publication date: 13 August 2010

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-008-9121-5

zbMATH Keywords

theta functionmodular equationRogers-Ramanujan functionsRogers-Ramanujan continued fractionRamanujan's lost notebook

Mathematics Subject Classification ID

Continued fractions (11A55) Applications of basic hypergeometric functions (33D90)

Related Items (16)

On Ramanujan's incomplete elliptic integral identities ⋮ Matching coefficients in the series expansions of certain \(q\)-products and their reciprocals ⋮ Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Göllnitz-Gordon functions and their associated continued fractions ⋮ Factorizations that involve Ramanujan's function \(k(q)=r(q)r^2(q^2)\) ⋮ On certain \(q\)-trigonometric identities analogous to that of Gosper's ⋮ “cases? for φ also” a question raised by Ramanujan ⋮ Some modular relations for Ramanujan's function \(k(q)=r(q)r^2(q^2)\) ⋮ Eisenstein series and elliptic functions on \(\Gamma _{0}(10)\) ⋮ On Ramanujan's function \(k(q)=r(q)r^{2}(q^{2})\) ⋮ An elementary approach to Eisenstein series identities of Huber, Schultz and Ye ⋮ Ramanujan's function \(k\), revisited ⋮ A new proof of Ramanujan's modular equation relating \(R(q)\) with \(R(q^{5})\) ⋮ Unnamed Item ⋮ On conjectures of Koike and Somos for modular identities for the Rogers–Ramanujan functions ⋮ 5-dissections and sign patterns of Ramanujan's parameter and its companion ⋮ Vanishing coefficients and identities concerning Ramanujan's parameters

Cites Work

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• On two identities of Ramanujan
• Some theorems on the Rogers-Ramanujan continued fraction and associated theta function identities in Ramanujan's Lost Notebook
• The Rogers-Ramanujan continued fraction
• Modular transformations of Ramanujan's fifth and seventh order mock theta functions
• The continued fractions found in the unorganized portions of Ramanujan’s notebooks
• Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
• Some Theorems on the Rogers–Ramanujan Continued Fraction in Ramanujan’s Lost Notebook
• Ramanujan’s forty identities for the Rogers-Ramanujan functions

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