A GAUSSIAN QUADRATURE FOR THE OPTIMAL EVALUATION OF INTEGRALS INVOLVING LORENTZIANS OVER A SEMIINFINITE INTERVAL - COMMENT

Gauss quadrature rules corresponding to weight functions (1 + x(2))(-n ) on the interval (0,infinity) have been proposed (R.P. Sagar, V.H. Sm ith Jr. and A.M. Simas, Comput. Phys. Commun. 62 (1991) 16) for the ev aluation of atomic momentum expectation values. In this comment it is shown that by using Gauss-Rational quadrature rules the results of Sag ar et al. can be improved considerably for higher accuracy demands. In addition, it is pointed out that up to now there is no sufficient pro of that their procedure is convergent. The usual proof for Gauss rules does not apply. The reason is that for weight functions of the above form a complete orthogonal system of polynomials is not available due to the divergence of the higher moment integrals.