Use of binomial coefficients in fast and accurate calculation of Lowdin-alpha radial functions

In the present paper, we introduce a new algorithm for the development of efficient numerical methods for the analytical solution of the Lowdin-alpha radial function. The final results are expressed through the binomial coefficients, which enable fast and accurate calculation of the Lowdin-alpha radial function. The comparisons of the obtained results with the literature have shown that the presented approach can be used for the fast calculation of multicenter multielectron integrals over Slater-type orbitals (STOs). The efficiency of the algorithm is discussed and its performance with several examples is demonstrated.