Evaluations of the cubic continued fraction by some theta function identities. (English) Zbl 1432.11047
Summary: In this paper, we use some theta function identities involving two parameters \(h_{n,k}\) and \(h'_{n,k}\) for the theta function \(\varphi\) to establish new evaluations of Ramanujan’s cubic continued fraction.
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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