THE CONVERGENCE OF PADÉ APPROXIMANTS TO FUNCTIONS WITH BRANCH POINTS

This paper describes the result of work on the convergence of diagonal Pade approximants to a class of functions with an even number of branch points with principal singularities of square root type. Convergence in capacity is shown away from a set of arcs whose location is completely determined by the location of the branch points. A conjecture about the possible form of extensions of this work is presented.