An explicit analytic solution to the Thomas-Fermi equation

In this paper, a newly proposed analytical scheme by the authors namely the improved di erential transform method is employed to provide an explicit series solution to the Thomas Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with di erentiation, and ends up in a recursive formula involving the Adomian polynomials to a ord the unknown coe cients. Unlike many other methods, our approach is free of integration and hence can be of computational interest. In addition, a very good agreement between the proposed solution and the results from several well-known works in the literature is demonstrated.