The maximum term of a power series - G. S. Srivastava; O. P. Juneja (International Journal of Mathematics and Mathematical Sciences)
Let ∑n=0∞anzλn 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.