I'm trying to understand the generalized Gaussian quadrature rules for singularities at one of the endpoints. For this I studied this paper by Daan Huybrechs.
On page 12 there are the plots for the functions $R_n$ and $S_n$ for $n = 0, ..., 4$. I tried to calculate the functions $R_n$ and $S_n$ for $\psi(x) = x^{1/3}$, also with the way explained in chapter 4.3, but I don't know how to calculate the quadrature points.
What is the correct way to calculate those points $x_j$?