APPLICATIONS OF THE ICOSAHEDRAL EQUATION FOR THE ROGERS-RAMANUJAN CONTINUED FRACTION

Let R(q) denote the Rogers-Ramanujan continued fraction for |q| < 1. Using expressions involving the theta function f(-q) := (q; q)∞ given in modular relations due to Yi, we introduce evaluations for $R(e^{-{\pi}{\sqrt{r}}})$, for r ∈ ℚ_>0. We prove our closed forms using the icosahedral equation for R together with closed forms for and modular relations associated with Ramanujan's G- and g-functions.