Extensions of Drummond's process for convergence acceleration

In this paper, we give some new algebraic properties of a sequence transformation due to Drummond for accelerating the convergence. In the particular case where the terms of the sequence to be transformed are the partial sums of a formal power series, this transformation leads to Padé-type approximants. Then, using various operators, some extensions of Drummond's process are proposed, and their properties are given. A new expression for the E-transformation, using generalized divided differences, is obtained, and it is also generalized. The recurrence relation for these differences can be used for its implementation, and the Ford–Sidi algorithm is also related to them. Lubkin's T and W-transformations, which could be related to Drummond's, are discussed in Appendix A.