On Ramanujan’s general theta function and a generalization of the Borweins’ cubic theta functions. (English) Zbl 1377.11048
Summary: The Borwein brothers have introduced and studied three cubic theta functions. Many generalizations of these functions have been studied as well. In this paper, we introduce a new generalization of these functions and establish general formulas that are connecting our functions and Ramanujan’s general theta function. Many identities found in the literature follow as a special case of our identities. We further derive general formulas for certain products of theta functions.
MSC:
| 11F27 | Theta series; Weil representation; theta correspondences |
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
| 05A30 | \(q\)-calculus and related topics |
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