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Using one-center expansion relations for the Slater type orbitals (STOs) ofnoninteger principal quantum numbers in terms of integer n STOs derived in thisstudy with the help of - exponential type orbitals (-ETOs, the general formulasare established for the unsymmetrical and symmetrical one-range additiontheorems of STOs and Coulomb-Yukawa like correlated interaction potentials(CIPs) with integer and noninteger indices. The final results are especiallyuseful for computations of arbitrary multicenter multielectron integrals overSTOs that arise in the Hartree-Fock-Roothaan (HFR) approximation and also inthe correlated methods which play a significant role in theory and applicationto quantum mechanics of atoms, molecules, and solids.

Unsymmetrical and symmetrical one-range addition theorems for Slater  type orbitals and Coulomb-Yukawa like correlated interaction potentials of  integer and noninteger indices