A new continued fraction of Ramanujan, its modular identities and explicit evaluations

DOI10.1007/s13370-013-0215-xzbMath1422.11011OpenAlexW2083730135MaRDI QIDQ2516931

Nipen Saikia

Publication date: 4 August 2015

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-013-0215-x

zbMATH Keywords

continued fractionmodular equationtheta-function

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Continued fractions (11A55) Continued fractions; complex-analytic aspects (30B70) Applications of basic hypergeometric functions (33D90)

Related Items

New theta-function identities and general theorems for the explicit evaluations of Ramanujan's continued fractions, Some \(q\)-continued fractions of Ramanujan, their explicit values, and equalities, Modularity of a certain continued fraction of Ramanujan, Three Ramanujan continued fractions with modularity

Cites Work

• Some new explicit values of quotients of theta-function \(\phi(q)\) and applications to Ramanujan's continued fractions
• Explicit evaluations of Ramanujan-Göllnitz-Gordon continued fraction
• 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
• Parametric evaluations of Ramanujan's singular moduli
• Ramanujan’s modular equations and Weber–Ramanujan class invariants G n and g n
• Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations
• Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
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