Note on the Convergence of Sequences of Rational Functions of Best Approximation to a Meromorphic Function - Walsh, Joseph L. (1972)
If the function f(z) is meromorphic at every finite point of the plane, analytic on C: [unk]z[unk] ≤ 1, there are results that can be established concerning the convergence of the sequence R(n)(z) of rational functions of each degree n of best approximation to f(z) on C. However, we need to assume certain additional conditions on the convergence of the sequence R(n)(z) itself. The results generalize to more general sets C and to more general functions.