An extension of the Levin-Sidi class of nonlinear transformations for accelerating convergence of infinite integrals and series

摘要

In this paper we extend Levin and Sidi's nonlinear D- and d-transformations for accelerating convergence of infinite integrals and series. The simple extension is made by viewing all these transformations as generalized jackknifes. The new transformations appear to be more accurate in general and are as easily implemented as D- and d-transformations. The new transformations have also some computational advantages. As a result more accurate approximations can be obtained in many cases, as is shown in the examples which are included.