Abstract
In his work, Ramanujan recorded a list of 40 beautiful modular relations for the Rogers–Ramanujan functions (RRFs) G(q) and H(q) and noted, enigmatically, that “Each of these formulae is the simplest of a large class.” Ramanujan did not shed light, and it appears to be a mystery about what precisely these classes are. Mathematicians from Ramanujan’s contemporaries, G. N. Watson and L. J. Rogers, noted modern mathematicians have sought to explore, prove, and find further relations for RRFs and analogues. Very recently, Bulkhali and Ranganatha have proved 24 new relations involving sums or differences of products of quadruples of RRFs rather than products of pairs of functions. In this article, we extend the list of modular relations involving RRFs by providing twenty-six new modular relations. We also discuss their applications to the theory of partitions.
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Acknowledgements
The first author’s research was supported by DST-Ph.D. Fellowship (No. DST/KSTePS/Ph.D. Fellowship/MAT-01:2021-22/1027) from the Government of Karnataka. The authors thank the referee for his/her several helpful comments.
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Communicated by Eknath Ghate.
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Channabasavayya, Keerthana, G.K. & Dasappa, R. On further modular relations for the Rogers–Ramanujan functions. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00458-3
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DOI: https://doi.org/10.1007/s13226-023-00458-3