three-electron integrals [@Per] in relative coordinates. The explicit symmetrizaton of the wave function upon all permutations of identical particles (electron) is discussed in detail in our earlier works (see, e.g., [@Fro2010] and references therein). Note also that all calculations in this work have been performed with the use of standard quadruple precision accuracy (30 decimal digits per computer word). In our calculations we have used variational wave functions for the Li atom, Be$^{+}$ and B$^{3+}$ ions with 60 terms. To construct these wave functions we follow the procedure described in detail in [@Fro2011].

As mentioned above in this study we consider the doublet $2^2S(L = 0)$-states in the three-electron Li atom and in analogous Be$^{+}$ and B$^{2+}$ ions. The corresponding expectation values (or properties) can be found in Table I (in atomic units $\hbar = 1, e = 1, m_e = 1$). For most of the properties mentioned in Table I their meaning is clear from the notation used. Therefore, here we can restrict ourselves to a few following remarks. All electron-nucleus properties are designated below with the use of a general index $eN$ (electron-nucleus), while the notation $ee$ stands for electron-electron properties. For instance, the notations $\langle r_{eN} \rangle$ 