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

New development in theory of Laguerre polynomials