  In this work a new expansions of Coulomb potential and interparticle
distance, linear term $r_{12}$ are proposed. Except the singularities, the
expansions converge to the exact value in the whole coordinate space including
the vicinity of the singularities or correlation cusps points. The disadvantage
of the expansion is, that it leads to complicated goniometric functional forms.
Anyway, for their simplification, we used the method of their expansion
developed by the author in the past.
