Some new general theorems for the explicit evaluations of the Rogers-Ramanujan continued fraction

DOI10.1007/s40315-013-0040-0zbMath1291.30021OpenAlexW2033462508MaRDI QIDQ2435437

Nipen Saikia

Publication date: 19 February 2014

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-013-0040-0

zbMATH Keywords

parametersexplicit evaluationRamanujan's theta-functionRogers-Ramanujan continued fraction

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Dedekind eta function, Dedekind sums (11F20) Continued fractions; complex-analytic aspects (30B70) Applications of basic hypergeometric functions (33D90)

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• Some new explicit values of the parameters \(s_n\) and \(t_n\) connected with Rogers-Ramanujan continued fraction and applications
• Explicit evaluations of Ramanujan-Göllnitz-Gordon continued fraction
• On some new general theorems for the explicit evaluations of Ramanujan's remarkable product of theta-functions
• Some theorems on the Rogers-Ramanujan continued fraction and associated theta function identities in Ramanujan's Lost Notebook
• Theta-function identities and the explicit formulas for theta-function and their applications
• Two parameters for Ramanujan's theta-functions and their explicit values
• Evaluations of the Rogers–Ramanujan continued fraction R(q) by modular equations
• On Ramanujan's continued fraction
• The continued fractions found in the unorganized portions of Ramanujan’s notebooks
• Ramanujan's remarkable product of theta-functions
• Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
• Some Values for the Rogers-Ramanujan Continued Fraction

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