Recent results relevant to the evaluation of infinite series

Abstract A review is made of recent results concerning the convergence properties of the Punctual Pade´Approximant method. The technique involves the use of Shanks' non-linear transformations of the sequence of partial sums of the series under consideration, which is actually equivalent to using ordinary Pade´approximants at a particular point. Previous theorems are extended and stated more generally, so that they may be of use in other areas, besides that of potential scattering theory for which they were originally intended. The results show the value of the approach as a convergence acceleration method when dealing with convergent series, and as a regularization procedure otherwise.