In this paper, global regularization method for planar restricted three-body
problem is purposed by using the transformation z = x+iy = ? cos n(u+iv),
where i = ??1, 0 < ? ? 1 and n is a positive integer. The method is developed
analytically and computationally. For the analytical developments, analytical
solutions in power series of the pseudotime ? are obtained for positions and
velocities (u, v, u', v') and (x, y, x?, y?) in both regularized and physical
planes respectively, the physical time t is also obtained as power series in
?. Moreover, relations between the coefficients of the power series are
obtained for two consequent values of n. Also, we developed analytical
solutions in power series form for the inverse problem of finding ? in terms
of t. As typical examples, three symbolic expressions for the coefficients of
the power series were developed in terms of initial values. As to the
computational developments, the global regularized equations of motion are
developed together with their initial values in forms suitable for digital
computations using any differential equations solver. On the other hand, for
numerical evolutions of power series, an efficient method depending on the
continued fraction theory is provided.