Set alpha=0 and plot all points and weights as a function of beta. Then let's choose 0 <= beta <= 12 and fit the curve to machine accuracy using minimax polynomial and generate Fortran code that stores these coefficients for each point and weight for a select Nq (the number of points). We'll start with Nq=64, and we can choose, maybe we can just do Nq = 1, 2, 4, 8, 16, 32, 64, or something like that.
Set alpha=0 and plot all points and weights as a function of beta. Then let's choose 0 <= beta <= 12 and fit the curve to machine accuracy using minimax polynomial and generate Fortran code that stores these coefficients for each point and weight for a select Nq (the number of points). We'll start with Nq=64, and we can choose, maybe we can just do Nq = 1, 2, 4, 8, 16, 32, 64, or something like that.