Angular Fock coefficients: Refinement and further development

The angular coefficients ψk,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 the hyperspherical harmonics Ykl, 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 the simplest nonseparable and separable right-hand sides are proposed. Some mistakes or misprints made earlier in representations of ψ2,0, are noted and corrected. All j components of ψ4,1 and the majority of components and subcomponents of ψ3,0 are calculated and presented. All calculations are carried out with the help of Wolfram Mathematica.