Majorana solution of the Thomas-Fermi equation

We report on an original method, due to Majorana, that leads to a semi-analytical series solution of the Thomas-Fermi equation with appropriate boundary conditions in terms of only one quadrature. We also deduce a general formula for such a solution that avoids numerical integration, but is expressed in terms of the roots of a polynomial equation. (C) 2002 American Association of Physics Teachers.