Calculation of atomic integrals using commutation relations

In this paper, a numerically stable method of calculating atomic integrals is suggested. The commutation relations among the components of the angular momentum and the Runge-Lenz vector are used to deduce recurrence relations for the Sturmian radial functions. The radial part of the one- and two-electron integrals is evaluated by means of these recurrence relations. The product of two radial functions is written as a linear combination of the radial functions. This enables us to write the integrals over four radial functions as a linear combination of the integrals over two radial functions. The recurrence relations for the functions are used to derive the recursion relations for the coefficients of the linear combination and for the integrals over two functions