Gaussian quadrature abscissae

It is well known that the determination of abscissas and weights of the Gaussian quadrature from power moments is an exponentially ill-conditioned problem due to the presence of rounding errors. 

Note that a different set of Laguerre polynomials, parameterized by k > 0, is used for each value of a. Thus, the weights and abscissas must be computed separately for each value of a. As with any Gaussian quadrature, Eq. (3.86) is exact when g(f) is a polynomial of order less than 2N (Gautschi, 2004). 

We have now developed a complete scheme for the evaluation of one-electron Coulomb integrals by Gaussian quadrature. First, we calculate (by some numerical scheme) the abscissae and weights... 

---