  We find approximate analytical presentation of the solutions $\Psi(r_1, r_2,
r_{12})$ of Schr\"odinger equation for two-electron system bound by the
nucleus, in the space region $r_{1,2}=0$ and $r_{12}=0$ that are of great
importance for a number of physical processes. The presentation is based on the
well known behavior of $\Psi(r_1, r_2, r_{12})$ near the singulartriple
coalescence point. The approximate functions are compared to the locally
correct ones obtained earlier by the Correlation Function Hyperspherical
Harmonic (CFHH) method for helium atom, light heliumlike ions and for the
negative ion of hydrogen $H^-$. The functions are shown to determine a natural
basis for the expansion of CFHH functions in the considered space region. We
demonstrate, how these approximate functions simplify the calculations of the
high energy ionization processes.
