[en] Punctual Pade Approximants are considered as a summation method of the slowly convergent partial wave expansions associated with the scattering by long range potentials. The asymptotic behaviour of the family of sequence [n, n+m], with fixed n, of the Pade table, is studied. A set of theorems are proven, which show that their rate of convergence increases rapidly with n. It is remarked that these approximants may be computed by means of the recurrent epsilon and eta algorithms