One-Range Addition Theorems in Terms of ??-ETOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices

The expansion formulas in terms of complete orthonormal sets of Psi(alpha)-exponential type orbitals are established for the Slater type orbitals and Coulomb-ukawa like correlated interaction potentials of integer and non integer indices. These relations are used in obtaining their unsymmetrical and symmetrical one-range addition theorems. The final results are especially useful in the calculations of multi centre multi electron integrals occurring when Hartree-Fock-Roothaan and explicitly correlated methods are employed.