New proofs of some Dedekind η-function identities of level 6

Raksha, H. M. Srivastava, N. V. Sayinath Udupa, B. R. Srivatsa Kumar

Research output: Contribution to journalArticlepeer-review


Recently, Shaun Cooper proved several interesting η-function identities of level 6 while finding series and iterations for 1/π. In this sequel, we present some new proofs of the η-function identities of level 6 discovered by Cooper. Here, in this article, we make use of the modular equation of degree 3 in two methods. We further give some interesting combinatorial interpretations of colored partitions. We also briefly describe a potential direction for further researches based upon some related recent developments involving the Jacobi’s triple-product identity and the theta-function identities as well as on several other q-functions which emerged from the Rogers-Ramanujan continued fraction R(q) and its such associates as G(q) and H(q). We point out the importance of the usage of the classical q-analysis and we also expose the current trend of falsely-claimed “generalization” by means of its trivial and inconsequential (p, q)-variation by inserting a forced-in redundant (or superfluous) parameter p.

Original languageEnglish
Pages (from-to)3755-3767
Number of pages13
Issue number12
Publication statusPublished - 2023

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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