On extension of a power series outside of its disk of convergence

The problem of computer extension of power series came from the papers by Milton Van Dyke in the 1970s and is related to the theory of perturbations in fluid mechanics. The seminal Stahl's Theory (1985-1986) provided the theoretical basis for the use of Pade approximations in solving this problem. The culmination of using Stahl's Theory is the development of HELM by Antonio Trias in 2012.
In the talk, we propose to discuss some other methods of power series extension based on rational Hermite-Pade approximations.