Punctual Padé approximants as a regularization procedure for divergent and oscillatory partial wave expansions of the scattering amplitude

Previous theorems on the convergence of the [n,n + m] punctual Padé approximants to the scattering amplitude are extended. The new proofs include the cases of nonforward and backward scattering corresponding to potentials having 1/r and 1/r2 long-range behaviors, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long-range potentials of interest in potential scattering. © 1978 American Institute of Physics.