On Value Distribution of Difference Polynomials of Meromorphic Functions

Zong-Xuan Chen

doi:10.1155/2011/239853

Abstract

We study the value distribution of the difference counterpartΔf(z)−af(z)noff′(z)−af(z)nand obtain an almost direct difference analogue of results of Hayman.

Highlights

Introduction and ResultsHayman proved the following Theorem A
Since σ G k1 < k and σ g < k, we see that the left hand side of 3.5 is of order k by applying the general form of the Valiron-Mohon’ko lemma in 10, a contradiction
G z g∗ z exp βzk, 3.6 where β / 0 is a constant, g∗ z /≡ 0 is an entire function satisfying σ g∗ < k

Summary

Introduction

Introduction and ResultsHayman proved the following Theorem A. Let f z be a transcendental entire function of finite order with a Borel exceptional value 0, and let a, c ∈ C \ {0} be constants, with c such that f z c /≡ f z .

Results

Conclusion