International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 2, Pages 239-250
Remainders of power series
1Department of Mathematics, LeMoyne–Owen College, Memphis 38126, Tennessee, USA
2Department of Mathematics, Wright State University, Dayton 45431, Ohio, USA
3Department of Mathematics, Los Alamos Scientific Laboratory, Los Alamos 87545, New Mexico, USA
Received 21 February 1978; Revised 20 March 1979
Copyright © 1979 J. D. McCall 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.
Suppose has radius of convergence and . Suppose , and is either or a neighborhood of . Put . Two questions are asked: (a) can be cofinite? (b) can be infinite? This paper provides some answers to these questions. The answer to (a) is no, even if . The answer to (b) is no, for if . Examples show (b) is possible if and for a neighborhood of .