TY - JOUR

T1 - New proofs of some Dedekind η-function identities of level 6

AU - Raksha,

AU - Srivastava, H. M.

AU - Sayinath Udupa, N. V.

AU - Srivatsa Kumar, B. R.

N1 - Publisher Copyright:
© 2023, University of Nis. All rights reserved.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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U2 - 10.2298/FIL2312755R

DO - 10.2298/FIL2312755R

M3 - Article

AN - SCOPUS:85150441133

SN - 0354-5180

VL - 37

SP - 3755

EP - 3767

JO - Filomat

JF - Filomat

IS - 12

ER -