Fast and accurate method for summation of divergent series

We develop a particular case of algebraic approximants for the summation of divergent power series and for the continuation of such expansions beyond their radius of convergence. The calculation of bound states and resonances for one- and two-dimensional anharmonic oscillators, for a perturbed rigid rotor, and for the Zeeman and Stark effects in hydrogen shows that the pre sent method is one of the most efficient ones for that purpose. (C) 2001 Jo hn Wiley & Sons, Inc.