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Subcomponents $ψ_{4,1}^{(2d)}$ and $ψ_{3,0}^{(2c)}$ of the angular Fock coefficients: Explicit analytic representation

The Fock expansion [1] describes the $S$-state wave function of the two-electron atomic system in the vicinity of the triple coalescence point. The present work constitutes the additional appendix to our paper [2] devoted to refinement and further development of calculation of the angular Fock coefficients of the Fock expansion. We derive the explicit analytic expressions for the complicated subcomponents $ψ_{4,1}^{(2d)}$ and $ψ_{3,0}^{(2c)}$ of the angular Fock coefficients. An unusual method of using the Wolfram Mathematica was applied.