Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer nSTOs derived in this study with the help of psi(a)-exponential type orbitals (psi(a)-ETOs, a = 1, 0,-1,-2, . . .), the general formulas through the integer nSTOs are established for the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb-Yukawa-like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for the computations of arbitrary multicenter multielectron integrals that arise in the Hartree-Fock-Roothaan (HFR) approximation and also in the correlated methods based upon the use of STOs as basis functions.