A new proof of Ramanujan's modular equation relating \(R(q)\) with \(R(q^{5})\)

DOI10.1007/S11139-009-9180-2zbMath1257.11093OpenAlexW2067285741MaRDI QIDQ1047810

Chadwick Gugg

Publication date: 6 January 2010

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

Full work available at URL: https://doi.org/10.1007/s11139-009-9180-2

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Continued fractions and generalizations (11J70) Continued fractions (11A55) Applications of basic hypergeometric functions (33D90) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (4)

Matching coefficients in the series expansions of certain \(q\)-products and their reciprocals ⋮ On the Andrews-Schur proof of the Rogers-Ramanujan identities ⋮ Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Göllnitz-Gordon functions and their associated continued fractions ⋮ Unnamed Item

Cites Work

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• Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Göllnitz-Gordon functions and their associated continued fractions
• Two modular equations for squares of the Rogers-Ramanujan functions with applications
• On the Rogers-Ramanujan continued fraction
• Ramanujan's continued fraction
• Ramanujan's ``lost notebook. III: The Rogers-Ramanujan continued fraction
• On the expansion of Ramanujan's continued fraction
• Some theorems on the Rogers-Ramanujan continued fraction and associated theta function identities in Ramanujan's Lost Notebook
• The Rogers-Ramanujan continued fraction
• Modular equations for the Rogers-Ramanujan continued fraction and the Dedekind eta-function
• On Ramanujan's continued fraction
• MacMahon's partition analysis XI: Broken diamonds and modular forms
• On recent congruence results of Andrews and Paule for broken k-diamonds
• 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
• On the divergence of the Rogers-Ramanujan continued fraction on the unit circle
• Some Theorems on the Rogers–Ramanujan Continued Fraction in Ramanujan’s Lost Notebook

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