Modular relations for the Rogers-Ramanujan functions with applications to partitions

DOI10.1007/s11139-020-00336-0zbMath1489.33015OpenAlexW3128534191MaRDI QIDQ2240490

Nasser Abdo Saeed Bulkhali, Ranganatha Dasappa

Publication date: 4 November 2021

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

Full work available at URL: https://doi.org/10.1007/s11139-020-00336-0

zbMATH Keywords

partitionstheta functionscolored partitionsRogers-Ramanujan functionsmodular relations

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)

Cites Work

• Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Göllnitz-Gordon functions and their associated continued fractions
• Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions
• A generalization of a modular identity of Rogers
• Basic functional equations of the Rogers-Ramanujan functions
• New identities for the Rogers–Ramanujan functions
• COMMON SOURCE OF NUMEROUS THETA FUNCTION IDENTITIES
• 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
• Some Identities Involving Rogers-Ramanujan-Type Functions
• Ramanujan’s forty identities for the Rogers-Ramanujan functions
• Ramanujan's Lost Notebook
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