A series solution to the Thomas–Fermi equation

Nonlinear Thomas–Fermi equation is solved by an analytic technique named homotopy analysis method (HAM) in this paper. For a further improvement of the convergence and precision of the solution to Thomas–Fermi equation by HAM, different from previous work, however, a more generalized set of basis function and consequential auxiliary linear operator are introduced to provide a series solution. The comparisons are also made among the results of the present work, some well-known numerical solution and previous work with the same technique, which shows the present work has provided a better series solution by far.