Geodesic
New proofs of some Dedekind η-function identities of level 6
Filomat, Tome 37 (2023) no. 12, p. 3755

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DOI

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.
DOI : 10.2298/FIL2312755R
Classification : 11F03, 14H42, 33C05
Keywords: Modular equations, Dedekind η-function, Theta functions, Basic (or q-) series and basic (or q-) identities, Combinatorial interpretations, Colored partitions, Rogers-Ramanujan continued fraction, Jacobi’s triple-product identity, Theta-function identities, Classical q-analysis and its trivial and inconsequential (p, q)-variation 
Raksha ; H M Srivastava; N V Sayinath Udupa; B R Srivatsa Kumar. New proofs of some Dedekind η-function identities of level 6. Filomat, Tome 37 (2023) no. 12, p. 3755 . doi: 10.2298/FIL2312755R
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     title = {New proofs of some {Dedekind} \ensuremath{\eta}-function identities of level 6},
     journal = {Filomat},
     pages = {3755 },
     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312755R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312755R/}
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