The asymptotic behavior of sequences and new series transformations based on the Cauchy product (Q1178576)

The first part of the paper consists of a review of known results concerning the asymptotic behavior of the ratio of the errors and the ratio of the differences for a convergent sequence, followed by a review of the same for a comparison of two convergent sequences, including some generalizations. Altogether 21 theorems are given. The final part of the paper studies convergence acceleration by old and new methods. The Cauchy-type series transformations introduced in the paper are proved to be Padé type approximants under certain conditions.