Abstract
In this paper, we investigate the value distribution of difference polynomial and obtain the following result, which improves a recent result of K. Liu and L.Z. Yang: Let f be a transcendental meromorphic function of finite order σ , c be a nonzero constant, and α(z) �≡ 0 be a small function of f ,a nd let P(z )= anz n + an-1z n-1 + ··· + a1z + a0
Highlights
1 Introduction and main results Throughout the paper, we assume that the reader is familiar with the standard symbols and fundamental results of Nevanlinna theory as found in [ – ]
A function f (z) is called the meromorphic function, if it is analytic in the complex plane except at isolated poles
For any non-constant meromorphic function f, we denote by S(r, f ) any quantity satisfying
Summary
Introduction and main resultsThroughout the paper, we assume that the reader is familiar with the standard symbols and fundamental results of Nevanlinna theory as found in [ – ]. For any non-constant meromorphic function f , we denote by S(r, f ) any quantity satisfying We denote by σ (f ) the order of a meromorphic function f (z), and denote by λ(f ) (λ( /f )) the exponent of convergence of the zeros (poles) of f (z). In , Laine and Yang [ ] investigated the value distribution of difference products of entire functions, and obtained the following result.
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