Some new modular relations for the Rogers-Ramanujan type functions of order eleven with applications to partitions

DOI10.1016/j.jnt.2015.06.019zbMath1400.11134OpenAlexW1219587986MaRDI QIDQ495295

D. Ranganatha, Chandrashekar Adiga, Nasser Abdo Saeed Bulkhali, Hari M. Srivastava

Publication date: 9 September 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.06.019

zbMATH Keywords

partitionstheta functionsRogers-Ramanujan functionsmodular relationsbasic (or \(q\)-) identitiesJacobi's triple-product identity

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Analytic theory of partitions (11P82) Applications of basic hypergeometric functions (33D90)

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Cites Work

• Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions
• A generalization of a modular identity of Rogers
• Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series
• A Proof of some identities of Ramanujan using modular forms
• A look back at Ramanujan's Notebooks
• An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli
• Ramanujan’s forty identities for the Rogers-Ramanujan functions
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