Convergence of a class of Borel-Pade-type approximants

In this paper it is proposed the use of a recently introduced set of rational functions, the so-called Pade-type approximants, to perform the analytic continuation of Borel transform into a cut complex plane. It is shown that, by choosing a suitable set of orthogonal generating polynomials, the convergence of the Borel-Pade-type approximation method can be rigorously proven