On rates of acceleration of extrapolation methods for oscillatory infinite integrals

The purpose of this work is to complement and expand our knowledge of the convergence theory of some extrapolation methods for the accurate computation of oscillatory infinite integrals. Specifically, we analyze in detail the convergence properties of theW- and -transformations of the author as they are applied to three integrals, all with totally different behavior at infinity. The results of the analysis suggest different convergence and acceleration of convergence behavior for the above mentioned transformations on the different integrals, and they improve considerably those that can be obtained from the existing convergence theories.