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A new rational analytic approximation to the solution of the Thomas-Fermi boundary value problem is presented. The approximation is a development of the original conception of J.C. Mason  and has been developed to reproduce the numerical work of Parand et al  , as far as proved feasible. The fit to the numerical data, by a basic collocation process applied to the rational approximation, proved excellent. Mathematics Subject Classification: 34A34, 34A45, 34B15, 34B40, 65L60doi:10.12988/jite.2018.823 fatcat:udyallw36fholjw2mafn5uamzi