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