Angular Fock coefficients. Fixing the errors, and further development

The angular coefficients $ψ_{k,p}(α,θ)$ of the Fock expansion characterizing the S-state wave function of the two-electron atomic system, are calculated in hyperspherical angular coordinates $α$ and $θ$. To solve the problem the Fock recurrence relations separated into the independent individual equations associated with definite power $j$ of the nucleus charge $Z$, are applied. The "pure" $j$-components of the angular Fock coefficients, orthogonal to of the hyperspherical harmonics $Y_{kl}$, are found for even values of $k$. To this end, the specific coupling equation is proposed and applied. Effective techniques for solving the individual equations with simplest nonseparable and separable right-hand sides are proposed. Some mistakes/misprints made earlier in representations of $ψ_{2,0}$, were noted and corrected. All $j$-components of $ψ_{4,1}$ and the majority of components and subcomponents of $ψ_{3,0}$ are calculated and presented for the first time. All calculations were carried out with the help of the Wolfram \emph{Mathematica}.

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