its right, while analogous operator with the index ‘$\leftarrow$’ acts on its left. The definition of the cusp operator based on Eq.(\[cusp3\]) has a number of advantages in applications. In particular, it allows one to obtain more accurate values of the electron-nucleus and electron-electron cusps with the use of relatively short wave functions. In this study to determine the numerical values of all cusps mentioned in this Section we used the cusp operators written in the form of Eq.(\[cusp3\]).

Basis of six-dimensional gaussoids
==================================

For three-electron atoms and ions there is another variational expansion which can be effective to perform accurate computations of low-lying bound states, e.g., the low-lying bound $S(L = 0)$- and $P(L = 1)$-states. The high efficiency of such an expansion for bound state computations is based on very simple and numerically stable formulas for all matrix elements needed in computations of the total energies of these states. This variational expansion was developed in the mid-1970 by Kolesnikov and his group (see, e.g., [@KT] and references therein). In general, this expansion is also represented in the form of Eq.(\[psi\]), but only radial functions are represented as linear combinations of the six-dimensional gaussoids, e.g., for $\psi_{L=0}(A; \bigl\{ r_{ij} 