Some questions related to the Rogers-Ramanujan continued fraction

The Rogers-Ramanujan continued fraction is defined by
$R(q) := q^{1/5}/(1 +q/(1 + q^2/(1+q^3 + …$
with $|q| 1$. In this talk, we will look at some results and open questions related to $R(q)$. We will also look at some related concepts, such as the Rogers-Ramanujan identities, $t$-cores, and boson-fermion
correspondence. Among other things, we will look at the following integral: $[√(4φ + 3 )]−φ = 1+exp(−1/5 \int_\alpha^1 [(1 − t)^5(1 − t^2)^5(1 − t^3)^5…]/[
(1 − t^5)(1 − t^{10})(1 − t^{15})…] dt/t )$
where $\alpha:= e^{-2\pi}$, and $φ := (1 +√5)/2$ is the Golden Ratio.