[1]涂 金,彭淑凤,饶冬飞.有限对数级亚纯函数与整函数的复合[J].江西师范大学学报(自然科学版),2018,(06):587-591.[doi:10.16357/j.cnki.issn1000-5862.2018.06.06]
 TU Jin,PENG Shufeng,RAO Dongfei.The Composition of Meromorphic Function and Entire Function of Finite Logarithmic Order[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(06):587-591.[doi:10.16357/j.cnki.issn1000-5862.2018.06.06]
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有限对数级亚纯函数与整函数的复合()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2018年06期
页码:
587-591
栏目:
复分析研究
出版日期:
2018-12-20

文章信息/Info

Title:
The Composition of Meromorphic Function and Entire Function of Finite Logarithmic Order
文章编号:
1000-5862(2018)06-0587-05
作者:
涂 金1 彭淑凤1饶冬飞2
1.江西师范大学数学与信息科学学院,江西 南昌 330022; 2.豫章师范学院数学与计算机学院,江西 南昌 330103
Author(s):
TU Jin1PENG Shufeng1RAO Dongfei2
1.College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China; 2.College of Mathematics and Computer Science,Yuzhang Normal University,Nanchang Jiangxi 330103,China
关键词:
整函数 亚纯函数 有限对数级 对数零点收敛指数
Keywords:
entire function meromorphic functions order finite logarithmic order logarithmic convergence exponent of zeros
分类号:
O 174.52
DOI:
10.16357/j.cnki.issn1000-5862.2018.06.06
文献标志码:
A
摘要:
利用值分布理论,对复合函数f(g(z))的增长性、零点收敛指数和极点收敛指数进行了研究,其中f(z)为有限对数级整函数或者亚纯函数,g(z)为有限级整函数,所得结果丰富和完善了已有的结果.
Abstract:
In this paper,the growth,zeros and poles of composite function f(g(z)) are studied by using the value distribution theory,where f(z) is a meromorphic or entire function of finite logarithmic order and g(z) is entire of finite order,and some results are obtained which enrich and improve some previous results.

参考文献/References:

[1] 杨乐.值分布理论及其新研究[M].北京:科学出版社,1982.
[2] 仪洪勋,杨重骏.亚纯函数唯一性理论[M].北京:科学出版社,1995.
[3] Tarasyuk R I.A theorem of Valiron-Titchmarsh type for entire functions of finite logarithmic order[J].(Ukrainian)Mat Stud,1995,124(5):31-38.
[4] Chern,Peter Tien Yu.On meromorphic functions with finite logarithmic order[J].Trans Amer Math Soc,2006,358(2):473-489.
[5] Chern,Peter Tien Yu,Kim In Su.Criteria of an entire series with finite logarithmic order[J].Taiwanese J Math,2011,15(1):331-336.
[6] Polya G.On an integral function of an integral function[J].J London Math Soc,1926,1(1):12-15.
[7] Clunie J.The composition of entire and meromorphic functions:mathematical essays dedicated to A. J. Macintyre[M].Athens,Ohio:Ohio University Press,1970:75-92.
[8] Goldstein R.On the growth of compositions of entire and meromorphic functions[J].J Analyse Math,1973,26(1):169-182.
[9] Edrei A,Fuchs W H J.On the zeros of f(g(z)) where f and g are entire functions[J].J Analyse Math,1964,12(1):243-255.
[10] Bergweiler W.On the nevanlinna characteristic of a composite function[J].Complex Variable Theory Appl,1988,10(2/3):225-236.
[11] Zheng Jianhua,Yang Chungchun.Estimate on the number of fix-points of composite entire functions[J].Complex Variables Theory Appl,1994,24(3/4):301-309.
[12] 廖良文,杨重骏.亚纯函数分解理论,动力系统和函数方程中的一些新的和未解决的老问题与猜想[J].江西师范大学学报:自然科学版,2017,41(3):242-247.
[13] 敖海龙.整函数与亚纯函数的复合函数的增长性[J].北京大学学报:自然科学版,1988,24(1):33-46.
[14] 孙建武,孙志荣.Polya定理的推广[J].佳木斯大学学报:自然科学版,2005,23(4):623-627.
[15] Tu Jin,Chen Zongxuan,Zheng Xiumin.Composition of entire functions with finite iterated Order[J].J Math Anal Appl,2009,353(1):295-304.
[16] 李效敏,仪洪勋,张学.涉及复合亚纯函数和不动点的亚纯函数的正规族[J].江西师范大学学报:自然科学版,2016,40(6):578-586.
[17] Tanmay B.On some growth analysis of composite entire and meromorphic functions from the view point of their relative(p,q)-th type and relative(p,q)-th weak type[J].Korean J Math,2018,26(1):23-41.

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备注/Memo

备注/Memo:
收稿日期:2018-06-25
基金项目:国家自然科学基金(11561031),江西省自然科学基金(20161BAB201020,20132BAB211002)和江西省教育厅基金(GJJ151331)资助项目.
作者简介:涂 金(1979-),男,江西鹰潭人,副教授,博士,主要从事复分析研究.E-mail:tujin2008@sina.com
更新日期/Last Update: 2018-12-20