A family of theta-function identities based upon \(R_{\alpha}\), \(R_{\beta}\) and \(R_M\)-functions related to Jacobi’s triple-product identity. (English) Zbl 1474.11111
Summary: We establish a set of two new relationships involving \(R_{\alpha}\), \(R_{\beta}\) and \(R_m\)-functions, which are based up Jacobi’s famous triple-product identity. We, also provide answer for an open problem of Srivastava, Srivastava, Chaudhary and Uddin, which suggest to find an inter-relationships between \(R_{\alpha}\), \(R_{\beta}\) and \(R_m(m\in\mathbb{N})\), \(q\)-product identities and continued-fraction identities.
MSC:
| 11F27 | Theta series; Weil representation; theta correspondences |
| 11P83 | Partitions; congruences and congruential restrictions |
| 05A17 | Combinatorial aspects of partitions of integers |
| 05A30 | \(q\)-calculus and related topics |
Keywords:
theta-function identities; \(R_m\)-functions; Jacobi’s triple-product identity; Ramanujan’s theta functions; \(q\)-product identities; Euler’s pentagonal number theorem; Rogers-Ramanujan continued fraction; Rogers-Ramanujan identitiesReferences:
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