Rate of pole detection using Padé approximants to polynomial expansions

Pad & eacute; approximations constructed from orthogonal and Faber polynomials on some compact set E E serve as tools to detect poles of an approximated function around the set E E . The goal of this article is to study the rate of such pole detection using indicators introduced by Gonchar (Poles of rows of the Pad & eacute; table and meromorphic continuation of functions, Sb. Math. 43 (1981), 527-546). Particularly, we compute the values of these indicators corresponding to our extensions of Pad & eacute; approximation for the poles of the approximated function within the domain of its meromorphy. Our computations extend the indicator formulas found in the article by Gonchar.