  In this study, the one-center expansion formulas in terms of complete
orthonormal sets of -exponential type orbitals (-ETOs,) are established for the
Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction
potentials (CIPs) of integer and noninteger indices. These relations are used
in obtaining the unsymmetrical and symmetrical one-range addition theorems for
STOs and Coulomb-Yukawa like CIPs. The final results are especially useful in
the calculations of multicenter multielectron integrals of STOs and CIPs
occurring when Hartree-Fock-Roothaan (HFR) and explicitly correlated method are
employed.
