Summation of partial wave expansions in the scattering by long range potentials. I

Abstract

Punctual Padé approximants are considered as a summation method of the slowly convergent partial wave expansions associated with the scattering by long range potentials. The asymptotic behavior of the family of sequences [n,n + m], with fixed n, of the Padé table, is studied. A set of theorems are proven, which show that their rate of convergence increases rapidly with n. It is noted that these approximants may be computed by means of the recurrent ε and η algorithms. © 1978 American Institute of Physics.