Meromorphic continuation of functions and arbitrary distribution of   interpolation points
  We characterize the region of meromorphic continuation of an analytic function $f$ in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of $f$. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary. 
Manuel Bello Hern\'andez and Bernardo de la Calle Ysern
math.CA