  The explicit analytic solution of the Thomas Fermi equation thorough a new
kind of analytic technique, namely the homotopy analysis method, was employed
by Liao (Appl. Math. Comp. 144, (2003)). However, the base functions and the
auxiliary linear differential operator chosen were such that the convergence to
the exact solution was fairly slow. New base functions and auxiliary linear
operator to form a better homotopy are the main concern of the present paper.
It is known that proper choice of base functions and auxiliary operator is
extremely significant in gaining the exact solution in order to reduce the
computational cost. The proposed homotopy here not only greatly reduces the
computational efforts by at least doubling the convergence of the homotopy
series, but also enlarges the convergence region of the homotopy series as
compared with that of Liao. Pade approximants to the obtained solutions
increase the accuracy even to a higher degree. To support this, the explicit
analytical expressions obtained using the proposed approach are compared with
the numerically computed ones and those of Liao.
