  A family of polynomial coupled function of $n$ degree is proposed, in order
to generalize the Levi-Civita regularization method, in the restricted
three-body problem. Analytical relationship between polar radii in the physical
plane and in the regularized plane are established; similar for polar angles.
As a numerical application, trajectories of the test particle using polynomial
functions of $2, 3,..., 8$ degree are obtained. For the polynomial of second
degree, the Levi-Civita regularization method is found.
