One-range Addition Theorems for Complete Sets of Modified Exponential Type Orbitals and Noninteger n Slater Functions in Standard Convention

Using the L (p l*) ‐generalized Laguerre polynomials L (p l*) ‐GLPs) and φ (p l*) ‐generalized exponential type orbitals φ (p l*) ‐GETOs) introduced by the author in standard convention, the one‐ and two‐center onerange addition theorems are established for the complete sets of Ψ(α*) ‐modified exponential type orbitals (Ψ(α*) ‐METOs) and noninteger n χ‐Slater type orbitals (χ‐NISTOs), where pl* = 2l + 2 ‐ α* and α* is the integer (α* = α, −∞ < α ≤2) or noninteger (α* ≠ α, −∞ < α* < 3) self‐frictional quantum number. It should be noted that the origin of the L (p l*) ‐GLPs, φ (p l*) ‐GETOs and Ψ(α*) ‐METOs, therefore, of the one‐range addition theorems presented in this work is the Lorentz damping or self‐frictional field produced by the particle itself. We have presented in standard convention the one‐range addition theorems for complete orthonormal sets of Ψ(α*) ‐modified exponential type orbitals with integer α*. Here α* is the integer (α* = α, −∞ < α ≤2) or noninteger (α* ≠ α, −∞ < α* < 3) self‐frictional quantum number.