Fock expansion for two-electron atoms. High order angular coefficients

The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients $\psi_{k,p}(\alpha,\theta)$ with the maximum possible value of subscript $p$ are calculated on examples of the coefficients with $5\leq k \leq 10$. The presented technique makes it possible to calculate such angular coefficients for any arbitrarily large $k$. The mentioned coefficients being leading in the logarithmic power series representing the Fock expansion may be indispensable for the development of simple methods for calculating the helium-like electronic structure. The theoretical results obtained are verified by other suitable methods. The Wolfram Mathematica is used extensively.