Majorana solution of the Thomas–Fermi equation

  title={Majorana solution of the Thomas–Fermi equation},
  author={Salvatore Esposito},
  journal={American Journal of Physics},
  • S. Esposito
  • Published 22 November 2001
  • Mathematics
  • American Journal of Physics
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. 

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