Some general theorems on the explicit evaluations of Ramanujan's cubic continued fraction. (Q1414324)

Let \[ \mu_n = \frac{1}{3\sqrt{3q}}\prod_{n\geq 1}\frac{(1-q^n)^6}{(1-q^{3n})^6}, \quad q=e^{-2\pi\sqrt{n/3}}. \] The authors discover various relations involving \(\mu_n\) and evaluate \(\mu_n\) for certain positive integers \(n\). The authors also study other expressions similar to \(\mu_n\) and derive analogous results for them. Most of their identities are derived using modular equations discovered recently by \textit{Jinhee Yi} [Ramanujan J. 5, No. 4, 377--384 (2001; Zbl 1043.11041); Acta Arith. 97, No. 2, 103--127 (2001; Zbl 0982.33010)].