In this paper we shall improve
upon the results by K. Faulstich, W. Luh and L. Tomm by (i) considering power
series representing other meromorphic functions f, (ii) using a regular weighted
means method D to obtain the overconvergence property and (iii) showing that D
has a universal property with respect to analytic continuation i.e. for every simply
connected region G which contains the open disc of convergence of the Maclaurin
series of f but no pole of f, there is a subsequence of the D-transform of the n-th
partial sums of the Maclaurin series of f that converges to f uniformly on compact
subsets of G.
