On the Majorana solution to the Thomas-Fermi equation

05/05/2021

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by   Francisco M. Fernández, et al.

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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.