Integral representation of the error and asymptotic error bounds for generalized Padé type approximants

In this paper we will give an integral representation of the error for the generalized Padé type approximants defined in Brezinski (1991). We will deduce some asymptotic upper bounds on the error of sequences of these approximants. As applications, we will consider functions defined by their expansions in some families of classical orthogonal polynomials and obtain for the corresponding approximants some results on the speed of convergence. Finally, we obtain some results on the asymptotic behaviour of the error of these approximants for generalized Stieltjes functions.