[PDF] Top 20 Value Distribution of the kth Derivatives of Meromorphic Functions

... Copyright © 2014 Pai Yang, Xiaojun Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, ... See full document

... Nevanlinna value distribution theory of meromorphic functions are used (see [, ...a meromorphic function f , we use S(r, f ) to denote any quantity satisfying S(r, f ) = o(T (r, f )) ... See full document

... a meromorphic function play key roles in the construction and applications of classical Nevanlinna ...the value distribution of zeros of difference operators that can be viewed as discrete analogues ... See full document

... a meromorphic function in the complex plane C and a ∈ C , we use the follow- ing notations frequently used in Nevanlinna theory (see [–]): m(r, f ), N(r, f ), m(r, a) = m(r, f–a  ), N(r, a) = N(r, f –a  ), ... See full document

... exceptional value, a transcendental meromorphic functions has at most two picard exceptional ...of value distributions of differential polynomials is Hayman conjecture ...transcendental ... See full document

... A meromorphic (respectively entire) function always means a non-constant function meromorphic (respectively analytic) in the complex ...of value distribution is concerned with the density of ... See full document

... We use C to denote the open complex plane, C (= C ∪ {∞}) to denote the extended com- plex plane, and ( ⊂ C ) to denote an angular domain. We will use the fundamental results and the standard notation of the Nevanlinna ... See full document

... : Value distribution of the difference opera- tor, Advances in Difference equations, ...and value sharing of meromorphic functions, ... See full document

... We use Nevanlinna’s value distribution theory of meromorphic functions (see [1, 2]) as the main tool in the whole paper. In what follows, the growth order of w(z) is represented by σ (w) and ... See full document

... Nevanlinna’s value distribution theory of meromorphic functions in C such as the first and second main theorems, and the common notations such as the charac- teristic function T(r, f ), the ... See full document

... own value distribution theory, Nevanlinna proved that a non-constant meromorphic function is uniquely determined by the inverse image of 5 distinct values (including the infinity) ... See full document

... in value distribution of difference operators of meromorphic functions (see ...of meromorphic functions, their shifts and difference operators (see ...the value ... See full document

... A meromorphic (respectively entire) function always means a non-constant function meromorphic (respectively analytic) in the complex ...of value distribution is concerned with the density of ... See full document

... f (z) = C tan(az + b) + Dz + E, a, b, C, D, E ∈ R . (1.5) Without the condition that f has only simple poles, there are further examples for which f, f 0 and f 00 have only real zeros and poles, such as (2 + tan z) 2 ... See full document

... asymptotic value of F lies on J , but is not a vertex of J, and such that the complement of J in C ∪ {∞} consists of two simply connected domains B 1 and B 2 , with 0 ∈ B 1 and ∞ ∈ B 2 ... See full document

... the value a CM(counting multiplicities) if f −a and g − a have the same zeros with the same multiplicites and we say that f and g share the value a IM(ignoring multiplicities) if we do not consider the ... See full document

... der meromorphic functions and entire functions; Jianming Chang [2] has con- firmed the conjecture for infinite order meromorphic functions for the first time, which is based on theory ... See full document

... Remark 1.7. In Theorem 1.5 if we take f and g to be two nonconstant entire functions, then the theorem is true for an integer n ≥ 12. So Theorem 1.5 improves Theorem 1.2. Remark 1.8. In Theorem 1.6 if we take f ... See full document

... of meromorphic functions in D, the multiplicity of all zeros and poles of f ∈ F is at least max { k  + d + , k + ...of functions f and g in F , P(f )f (k) and P(g)g (k) share p(z) in D, then F is ... See full document

... Abstract In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function.. Ke[r] ... See full document