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The Fock expansion [1] describes the $S$-state wave function of thetwo-electron atomic system in the vicinity of the triple coalescence point. Thepresent work constitutes the additional appendix to our paper [2] devoted torefinement and further development of calculation of the angular Fockcoefficients of the Fock expansion. We derive the explicit analytic expressionsfor the complicated subcomponents $\psi_{4,1}^{(2d)}$ and $\psi_{3,0}^{(2c)}$of the angular Fock coefficients. An unusual method of using the WolframMathematica was applied.

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