关于无穷级亚纯函数

数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 750-762.

关于无穷级亚纯函数

张洪申, 葛玉丽

南阳师范学院数学与统计学院河南南阳 473061

收稿日期:2015-12-30 修回日期:2016-06-03 出版日期:2016-08-26 发布日期:2016-08-26
作者简介:张洪申,hongshenzhang@163.com
基金资助:
河南省自然科学基金（142300410385）和南阳师范学院科研基金（STP2015002）资助

On Meromorphic Functions of Infinite Order

Zhang Hongshen, Ge Yuli

Department of Mathematics and Statistics, Nanyang Normal University, Henan Nanyang 473061

Received:2015-12-30 Revised:2016-06-03 Online:2016-08-26 Published:2016-08-26
Supported by:
Support by the Natural Science Foundation of Henan Province(142300410385) and the Research Funds of Nan Yang Normal University(STP2015002)

摘要/Abstract

摘要：

用角域内的Nevanlinna理论与型函数，研究了无穷级亚纯函数的值分布，得到了无穷级亚纯函数存在涉及小函数的精确级Borel方向与Hayman方向，同时证明了无穷级亚纯函数存在涉及小函数的T方向与Hayman-T方向. 所得结果使现有无穷级的结果为推论.

关键词: 亚纯函数, 型函数, Borel方向, Hayman方向, T方向, Hayman-T方向

Abstract:

By using Nevanlinna theory of the angular domain and the type function of characteristic T(r,f), we study the value distribution of meromorphic functions of infinite order, obtain the existences of Borel direction and Hayman direction of proximate order dealing with small functions, at the same time prove existences of T direction and Hayman-T direction dealing with small functions, from which we can easily deduce the existing results.

Key words: Meromorphic function, Type functon, Borel direction, Hayman direction, T direction, Hayman-T direction

中图分类号:

O174.55

张洪申, 葛玉丽. 关于无穷级亚纯函数[J]. 数学物理学报, 2016, 36(4): 750-762.

Zhang Hongshen, Ge Yuli. On Meromorphic Functions of Infinite Order[J]. Acta mathematica scientia,Series A, 2016, 36(4): 750-762.

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