On the convergence of type I Hermite-Pad\'e approximants for a class of   meromorphic functions
  We study the convergence of type I Hermite-Pad\'e approximation for a class of meromorphic functions obtained by adding a vector of rational functions with real coefficients to a Nikishin system of functions. 
G. L\'opez Lagomasino, S. Medina Peralta
math.CV