On Rogers-Ramanujan-Slater type theta function identity. (English) Zbl 1539.11136
For \(0<q<1\), the functions \(\varphi(q)\) and \(\phi_0(q)\) are defined as follows: \(\varphi(q):=\sum_{n=-\infty}^\infty q^{n^2}\), \(\phi_0(q):=\sum_{n=0}^\infty q^{n^2}(-q;q^2)_n\), where \((a;q)_n=\prod_{k=0}^{n-1}(1-aq^k)\).
From the authors’ abstract: “The main purpose of this article is to prove two Rogers-Ramanujan-Slater type theta function identities related to \(\varphi(q)\) and \(\phi_0(q)\), which were earlier investigated by two legendary mathematicians of their time.”
From the authors’ abstract: “The main purpose of this article is to prove two Rogers-Ramanujan-Slater type theta function identities related to \(\varphi(q)\) and \(\phi_0(q)\), which were earlier investigated by two legendary mathematicians of their time.”
Reviewer: Ljuben Mutafchiev (Sofia)
MSC:
| 11P84 | Partition identities; identities of Rogers-Ramanujan type |
| 11F27 | Theta series; Weil representation; theta correspondences |
| 05A30 | \(q\)-calculus and related topics |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
| 33D15 | Basic hypergeometric functions in one variable, \({}_r\phi_s\) |
| 33D45 | Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) |
| 33D60 | Basic hypergeometric integrals and functions defined by them |
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 39B32 | Functional equations for complex functions |
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