  The new complete orthonormal sets of -Laguerre type polynomials (-LTP,) are
suggested. Using Schr\"odinger equation for complete orthonormal sets of
-exponential type orbitals (-ETO) introduced by the author, it is shown that
the origin of these polynomials is the centrally symmetric potential which
contains the core attraction potential and the quantum frictional potential of
the field produced by the particle itself. The quantum frictional forces are
the analog of radiation damping or frictional forces suggested by Lorentz in
classical electrodynamics. The new -LTP are complete without the inclusion of
the continuum states of hydrogen like atoms. It is shown that the nonstandard
and standard conventions of -LTP and their weight functions are the same. As an
application, the sets of infinite expansion formulas in terms of -LTP and
L-Generalized Laguerre polynomials (L-GLP) for atomic nuclear attraction
integrals of Slater type orbitals (STO) and Coulomb-Yukawa like correlated
interaction potentials (CIP) with integer and noninteger indices are obtained.
The arrange and rearranged power series of a general power function are also
investigated. The convergence of these series is tested by calculating concrete
cases for arbitrary values of parameters of orbitals and power function.
