International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 341-346
The maximum term of a power series
1Department of Mathematics, University of Roorkee, Roorkee, India
2Department of Mathematics, Indian Institute of Technology, Kanpur, India
Received 30 March 1984
Copyright © 1986 G. S. Srivastava and O. P. Juneja. 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.
Let be a power series, representing an analytic function in the disc . 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 to be of perfectly regular growth has been obtained.