RATIONAL-APPROXIMATIONS FROM THE D-TRANSFORMATION

Recently the authors have presented the d-transformation which has proved to be very efficient in accelerating the convergence of a large class of infinite series. In this work the d-transformation is modified in a way that suits power series. An economical method for computing the rational approximations arising from the modified transformation is developed. Some properties of these approximants, similar to those of the PadCrossed D sign © approximants, are derived. In the course of development a class of power series to which these rational approximations can be applied efficiently is characterized. A numerical example, showing the strong convergence properties of the approximations is appended and a comparison with the corresponding PadCrossed D sign.