. N A ] 2 5 N ov 2 00 4 On the Set of Uniform Convergence for the Last Intermediate Row of the Padé Table

Let a(z) be a meromorphic function having in the disk |z| < R precisely λ poles. In this work for the (λ−1)th row of the Padé table of a(z) the set of uniform convergence is explicitly obtained. The present note is a supplement to the previous work of the author (J. Approx. Theory, 123(2003), 160-207). In the theory of uniform convergence of the Padé approximants the principal question is if the presence of limit points of poles for a sequence of the Padé approximants in the disk D is the unique obstraction for the unuform convergence of the sequence on compact subsets of D. For the diagonal sequence the affirmative answer has been given (under some normality conditions) by A.A. Gončar [1]. In the paper [2] it was found all limit points of poles of the Padé approximants for the row known as the last intermediate row of the Padé table for a meromorphic function. In the present note we are going to show that limit points of poles for this row are also the unique obstraction for the uniform convergence. Thus taking into account the results of [2] we can obtain the set of uniform convergence for the last intermediate row. Recall relevant definitions and statements. Let a(z) be a function which is meromorphic in the diskDR = {