Accurate calculation of the solutions to the Thomas-Fermi equations
  We obtain highly accurate solutions to the Thomas-Fermi equations for atoms and atoms in very strong magnetic fields. We apply the Pad\'e-Hankel method, numerical integration, power series with Pad\'e and Hermite-Pad\'e approximants and Chebyshev polynomials. Both the slope at origin and the location of the right boundary in the magnetic-field case are given with unprecedented accuracy. 
Paolo Amore, John P. Boyd and Francisco M. Fern\'andez
quant-ph