An investigation of the applicability of the Padé approximant method

AbstractWe investigate by means of analysis and numerical examples the range of applicability of the Padé approximant method. We conclude that at least a subsequence of the [N, N] Padé approximants for f(z) converge uniformly to f(z) in any closed, connected set on the Riemann sphere containing the origin but not containing any of the singular points or points on suitable cuts of f(z). There are, however, certain types of singular points at which convergence does occur