International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 335-344

On rational approximation in a ball in N

P. W. Darko,1,2 S. M. Einstein-Matthews,1 and C. H. Lutterodt1

1Department of Mathematics, Howard University, 2441 6th Street, N. W. Washington D. C 20059, USA
2Department of Mathematics, Lincoln University, 19352, PA, USA

Received 9 July 1998

Copyright © 2000 P. W. Darko et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study rational approximations of elements of a special class of meromorphic functions which are characterized by their holomorphic behavior near the origin in balls in N by means of their rational approximants. We examine two modes of convergence for this class: almost uniform-type convergence analogous to Montessus-type convergence and weaker form of convergence using capacity based on the classical Tchebychev constant. These methods enable us to generalize and extend key results of Pommeranke and Gonchar.