Padé-type approximants and a summability theorem by Eiermann (Q1185969)

The authors give a simple proof of a result by \textit{M. Eiermann} [J.Comput. Appl. Math. 10, 219-227 (1984; Zbl 0538.65011)]\ concerning the convergence of Padé-type approximants with prescribed denominators (Eiermann extended an old summability theorem due to \textit{Y. Okada} [Math. Z. 23, 62-71(1925)]). The method uses an integral representating the error of approximation and furnishes easily proved alternative convergence results in a very elegant manner.