On the Maximum Term and Central Index of Entire Functions and Their Derivatives

Jianren Long,Zhigao Qin

doi:10.1155/2018/7028597

Abstract

We shall establish some criteria on entire series with finite logarithmic order in terms of maximum term and central index.

Highlights

A function f is called meromorphic, if it is nonconstant and analytic in the complex plane C except at possible isolated poles
We assume that the reader is familiar with the standard notation and fundamental results in Nevanlinna theory of meromorphic functions; see [1, 2] or [3] for more details
We often use the order of growth and the lower order of growth to measure the growth of a meromorphic function

Summary

Introduction

A function f is called meromorphic, if it is nonconstant and analytic in the complex plane C except at possible isolated poles. We often use the order of growth and the lower order of growth to measure the growth of a meromorphic function. For a meromorphic function f in C, the order of growth and the lower order of growth of f are defined by log T (r, f). If f is entire function in C, the order and lower order of f are defined by log M(r, f); i.e., T(r, f) is replaced with log M(r, f) in above equalities, where M(r, f) = max|z|=r|f(z)|. 10], the order and lower order are same by definition of T(r, f) and log M(r, f): T (r, f) By the following inequalities which can be found in [3, p. 10], the order and lower order are same by definition of T(r, f) and log M(r, f): T (r, f)

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