超级有穷条件下涉及超越亚纯函数导函数的亏量和的一个结果  

A Result Concerning the Deficiency Sums of Derivatives of Transendental Meromorphic Functions of Finite Hyper-Order

作　　者：李效敏[1] 袁前前 LI Xiao-Min;YUAN Qian-Qian(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2018年第A02期241-244,共4页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11461042);山东省自然科学基金项目(ZR2014AM011)资助~~

摘　　要：本文证明了下述结果:设f是复平面上的1个超级有穷且正规增长的超越亚纯函数,k是1个正整数,那么∑ sum (δ(a,f^((k)))) from a∈C≤2-(2k(1-Θ(∞,f))/(1+k(1-Θ (∞,f)))。该结果推广了杨乐[4]研究的有关结果,并举例说明该结果是最佳的。The questions related to the sum of deficiencies of the derivatives of transcendental meromorphic functions is one reseach topic attracted by the complex specialists in the world.In this paper,we will prove:∑a∈Cδ(a,f^(k))≤2-2k(1-Θ(∞,f))/1+k(1-Θ(∞,f)).where f is a transcendental meromorphic function of finite hyper-order andnormal growth,k is a positive integer.The result in this paper generalizes the corresponding result from Yang Lo[4].Examples are provided to show that the results in this paper,in a sense,are best possible.

关 键 词：亚纯函数 正规增长 亏量和 超级 

分 类 号：O174.52[理学—数学]