A user-friendly extrapolation method for oscillatory infinite integrals

Abstract

In a recent publication [4] the author developed an extrapolation method, the <italic>W</italic>-transformation, for the accurate computation of convergent oscillatory infinite integrals. In yet another publication [6] this method was shown to be applicable to divergent oscillatory infinite integrals that are defined in the sense of summability. The application of the <italic>W</italic>-transformation involves some asymptotic analysis of the integrand as the variable of integration tends to infinity. In the present work the <italic>W</italic>-transformation is modified so as to keep this asymptotic analysis to a minimum, involving only the phase of oscillations. This modified version, which turns out to be as efficient as the original <italic>W</italic>-transformation, can also be applied to convergent or divergent oscillatory infinite integrals other than those dealt with in [4] and [6]. The convergence properties of the modified transformation are analyzed in detail for the integrals of [4] and [6], and numerical examples are provided.