On the Majorana solution to the Thomas-Fermi equation
Francisco M. Fernández, Javier Garcia
TL;DR
The solution to the Thomas-Fermi equation discovered by Majorana is analysed and it is shown that the series for the slope at origin enables one to obtain results of accuracy far beyond those provided by available methods.
Abstract
We analyse the solution to the Thomas-Fermi equation discovered by Majorana. We show that the series for the slope at origin enables one to obtain results of accuracy far beyond those provided by available methods. We also estimate the radius of convergence of this series and conjecture that the singularity closest to origin is a square-root branch point.