On evaluations of the cubic continued fraction by modular equations of degree 3 revisited. (English) Zbl 07902306
Summary: We derive modular equations of degree 3 to find corresponding theta-function identities. We use them to find some new evaluations of \(G(e^{- \pi \sqrt{n}})\) and \(G(-e^{- \pi \sqrt{n}})\) for \(n=\frac{25}{3 \cdot 4^{m-1}}\) and \(\frac{4^{1-m}}{3 \cdot 25}\), where \(m = 0, 1, 2\).
MSC:
| 11F27 | Theta series; Weil representation; theta correspondences |
| 33C90 | Applications of hypergeometric functions |
| 11F20 | Dedekind eta function, Dedekind sums |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 33C75 | Elliptic integrals as hypergeometric functions |
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