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We obtain highly accurate solutions to the Thomas-Fermi equations for atomsand atoms in very strong magnetic fields. We apply the Pad\'e-Hankel method,numerical integration, power series with Pad\'e and Hermite-Pad\'e approximantsand Chebyshev polynomials. Both the slope at origin and the location of theright boundary in the magnetic-field case are given with unprecedentedaccuracy.

Accurate calculation of the solutions to the Thomas-Fermi equations