International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 614283 |

G. S. Srivastava, O. P. Juneja, "The maximum term of a power series", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 614283, 6 pages, 1986.

The maximum term of a power series

Received30 Mar 1984


Let n=0anzλn be a power series, representing an analytic function f(z) in the disc |z|<R. A characterization for the type of such functions was obtained by the authors [J. Math. Anal. Appl. 81(1981), 1-7] in terms of the maximum term and rank. It is proved in this paper by means of an example, that a similar relation does not hold in general for lower type and sufficient conditions have been obtained for the validity of the corresponding result for lower type. Alternative coefficient characterization for type and lower type have been given and a necessary and sufficient condition for the analytic function f(z) to be of perfectly regular growth has been obtained.

Copyright © 1986 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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