New theta function identities for a continued fraction of Ramanujan and their applications

DOI10.1007/S13370-020-00823-ZzbMath1488.11103OpenAlexW3080612674MaRDI QIDQ2035896

Nipen Saikia, Chayanika Boruah

Publication date: 25 June 2021

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

Full work available at URL: https://doi.org/10.1007/s13370-020-00823-z

zbMATH Keywords

Ramanujan's continued fractionexplicit evaluationreciprocity formulastheta-function identities

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Applications of basic hypergeometric functions (33D90)

Cites Work

• A product of theta-functions analogous to Ramanujan's remarkable product of theta-functions and applications
• Some new explicit values of quotients of theta-function \(\phi(q)\) and applications to Ramanujan's continued fractions
• A parameter for Ramanujan's function \(\chi(q)\): its explicit values and applications
• Modular relations and explicit values of Ramanujan-Selberg continued fractions
• Explicit evaluations of Ramanujan-Göllnitz-Gordon continued fraction
• Theta-function identities and the explicit formulas for theta-function and their applications
• Two parameters for Ramanujan's theta-functions and their explicit values
• The explicit formulas and evaluations of Ramanujan's theta-function \(\psi\)
• Ramanujan's Schläfli-type modular equations and class invariants \(g_n\)
• Ramanujan’s modular equations and Weber–Ramanujan class invariants G n and g n
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