The exact calculation of the edge components of the angular Fock coefficients

The present paper constitutes the development of our previous work devoted to calculations of the angular Fock coefficients, ${\psi }_{k,p}(\alpha ,\theta )$. The explicit analytic representations for the edge components ${\psi }_{k,0}^{(0)}$ and ${\psi }_{k,0}^{(k)}$ with $k\le 8$ are derived. The methods developed enable such a calculation for arbitrary $k$. The single-series representation for subcomponent ${\psi }_{3,0}^{(2e)}$ missed in the previous paper is developed. It is shown how to express some of the complicated subcomponents through the hypergeometric and the elementary functions, as well. Using the specific operator of the Wolfram Mathematica, the simple explicit representations for some complex mathematical objects under consideration are obtained.