Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability (Q1096824)

In a previous paper (Math. Comp. 38, 517-529 (1982; Zbl 0508.65011) the author develops an extrapolation procedure named W-transformation for numerically evaluating the infinite integrals \(\int^{\infty}_{a}f(t)dt\), \(a\geq 0\), where f is integrable at infinity. The author considers the problem of numerically evaluating the divergent integrals \(\int^{\infty}_{a}f(t)dt\), \(a\geq 0\), where f is not integrable at infinity. These integrals are defined in the sense of Abel summability. The author shows that the W-transformation can be used in evaluating these integrals efficiently.