  We calculate the pair distribution function, $g(r)$, in a two-dimensional
electron gas and derive a simple analytical expression for its value at the
origin as a function of $r_s$. Our approach is based on solving the
Schr\"{o}dinger equation for the two-electron wave function in an appropriate
effective potential, leading to results that are in good agreement with Quantum
Monte Carlo data and with the most recent numerical calculations of $g(0)$. [C.
Bulutay and B. Tanatar, Phys. Rev. B {\bf 65}, 195116 (2002)] We also show that
the spin-up spin-down correlation function at the origin, $g_{\uparrow
\downarrow}(0)$, is mainly independent of the degree of spin polarization of
the electronic system.
