期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1979
卷号：2
DOI：10.1155/S0161171279000223
出版社：Hindawi Publishing Corporation
摘要：Suppose ∑n=0∞anzn has radius of convergence R and σN(z)=|∑n=N∞anzn|. Suppose |z1|<|z2|<R, and T is either z2 or a neighborhood of z2. Put S={N|σN(z1)>σN(z) for zϵT}. Two questions are asked: (a) can S be cofinite? (b) can S be infinite? This paper provides some answers to these questions. The answer to (a) is no, even if T=z2. The answer to (b) is no, for T=z2 if liman=a≠0. Examples show (b) is possible if T=z2 and for T a neighborhood of z2.
