Some numerical results on the convergence of integral approximants (Q809539)

The paper deals with integral approximants (a special case of Hermite- Padé approximants of Latin type). These are used for example in the analysis of power series for test functions out of certain classes. The author reports on existing theorems pointing out various function classes as particularly appropriate for study and on numerical results indicating the expected rate of convergence. Usually these numerical experiments show diagonal types of approximants to converge faster than horizontal ones. Finally, comparison with other methods like contour method of estimating confluent singularities indicates the difference to be not great in general.