Some limiting cases of the 𝐺-transformation

Abstract

In this paper some new nonlinear transformations are introduced. They arise from considering the limit of the G G -transformation as a particular parameter approaches its limiting value. The primary purpose of these transformations is to increase the rate of convergence of an improper integral. However, by introduction of an iteration method it is shown that they may also be used to produce approximating functions for the tail of an improper integral. Several examples are included.