Self-Friction Power Series and Their Use for Construction of One-Range Addition Theorems of Noninteger Slater Functions and Coulomb–Yukawa Like Potentials

Using complete orthogonal \( \mathcal{L}^{{\left( {p_{l}^{*} } \right)}} \)-self-friction polynomials (\( \mathcal{L}^{{\left( {p_{l}^{*} } \right)}} \)-SFPs) in standard convention introduced by the author, the formulas for transformation of noninteger type functions to the power series are presented, where \( p_{l}^{*} = 2l + 2 - \alpha^{*} \) and α * is the integer (\( \alpha^{*} = \alpha ,\; - \infty < \alpha \le 2 \)) or noninteger (\( \alpha^{*} \ne \alpha ,\; - \infty < \alpha^{*} < 3 \)) SF quantum number. With the help of these power series, the one-center one-range addition theorems for χ-Slater type orbitals and V-Coulomb–Yukawa like potentials with noninteger indices (χ-NISTOs and V-NICYPs) are established. As an application, the atomic nuclear attraction integrals of χ-NISTOs and V-NICYPs are investigated.