Screening of macroions in colloidal plasmas: Accurate analytical solution of the Poisson-Boltzmann equation

Accurate analytical solution of the Poisson-Boltzmann equation in the cases of spherical and axial symmetries and planar problem is found. It is expressed by logarithm of power series presented in three different forms. For each of them the recurrence relations between the series coefficients are derived. Identity to the earlier known result for the planar problem is shown. Convergence of the power series in different cases is discussed.