The expansion formulas in terms of complete orthonormal sets of ψα-exponential type orbitals are established for the Slater type orbitals and Coulomb-Yukawa-like correlated interaction potentials of integer and noninteger 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 multicentre multielectron integrals occurring when Hartree-Fock-Roothaan and explicitly correlated methods are employed.