The denominator of Padé approximants of functions of Markov-Stieltjes type are closely connected to orthogonal polynomials which leads to control of the location of the poles and to convergence of the approximants. We investigate to which extent the convergence also holds for Padé-type approximants where the location of the poles is changed.

Padé-type approximants are rational functions with some preassigned poles whose power series expansion coincides with that of a given series as far as possible. The main open question for these approximants is the choice of the poles in order to obtain interesting approximation and convergence results. In this paper, the authors study this problem for functions of the Markov-Stieltjes type, when some of the poles are -1 and +1 with arbitrary multiplicities and points in the union of (-∞,-1) and (1,∞) with even multiplicities.