International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1979 / Article

Open Access

Volume 2 |Article ID 980820 | https://doi.org/10.1155/S0161171279000223

J. D. McCall, G. H. Fricke, W. A. Beyer, "Remainders of power series", International Journal of Mathematics and Mathematical Sciences, vol. 2, Article ID 980820, 12 pages, 1979. https://doi.org/10.1155/S0161171279000223

Remainders of power series

Received21 Feb 1978
Revised20 Mar 1979

Abstract

Suppose n=0anzn has radius of convergence R and σN(z)=|n=Nanzn|. 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=a0. Examples show (b) is possible if T=z2 and for T a neighborhood of z2.

Copyright © 1979 Hindawi Publishing Corporation. 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.


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