Overconvergence of subsequences of rows of Padé approximants with gaps

The block structure of the Padé table associated with a formal power series is well known. We study the analytic properties of the given power series in the case that as we travel along a row of the corresponding table, we encounter blocks of increasing size. Thus, we extend to row sequences of Padé approximants some classical results due to Hadamard and Ostrowski related with the overconvergence of subsequences of Taylor polynomials and the analytic properties of the limit function under the presence of gaps in the power series.