涉及例外函數(shù)的亞純函數(shù)族

李三華，吳高翔

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涉及例外函數(shù)的亞純函數(shù)族

*李三華，吳高翔

(井岡山大學(xué)數(shù)理學(xué)院，江西，吉安 343009)

通過(guò)研究涉及例外函數(shù)的亞純函數(shù)族，推廣了由Montel建立的一個(gè)正規(guī)定則，進(jìn)而得到了相應(yīng)亞純函數(shù)族的正規(guī)定則。由此把例外值推廣至例外函數(shù)的情形。

亞純函數(shù)；例外函數(shù)；正規(guī)族

Montel首先把函數(shù)族的正規(guī)性與函數(shù)的取值問(wèn)題聯(lián)系起來(lái)，得到了經(jīng)典的Montel定則[1]。

龐學(xué)誠(chéng)和L.zalcman[2]對(duì)Montel定則做過(guò)一定的研究。如今我們將Montel定則由例外值推廣至例外函數(shù)的情形，得到如下結(jié)果：

1 引理

2 定理的證明

[1] Montel P. Lecons sur familles mormales ed fonctions analytiques et leurs applications[M]. Gauthier-Villars, Pares,1927.

[2] Pang Xuecheng, Zalcman L. Normal families of meromorphic functions with multiple zeros and poles [J]. Israel J,Math, 2003, 136: 1-9.

[3] Gu Yongxing, Pang Xuecheng Fang Mingliang. The theory of normal family and its application[M]. Beijing:Science Press, 2002, 24.

[4] Schiff J. Normal families [M]. New York：Springer, 1993: 75-76.

[5] Pang Xuecheng, Zalcman L. Normal families and shared values [J]. Bull London Math Soc, 2000, 32: 325-331.

[6] 顧永興,龐學(xué)誠(chéng),方明亮. 正規(guī)族理論及其應(yīng)用 [M]. 北京: 科學(xué)出版社, 2007.

NORMAL FAMILIES OF MEROMORPHIC FUNCTION ASSOCIATED WITH OMITTED FUNCTIONS

*LI San-hua，WU Gao-xiang

(School of Mathematics and Physics, Jinggangshan University, Ji’an, Jiangxi 343009, China)

We study the family of meromorphic functions related to omitted functions and the promotion of a normal criteria established by Montel. Furthermore, we obtain the corresponding normal criterion of meromorphic functions, which can promote the omitted values to omitted functions situation.

meromorphic function; omitted function; normality

1674-8085(2014)01-0008-03

O174.52

A

10.3969/j.issn.1674-8085.2014.01.002

2013-09-24；

2013-10-26

吉安市科技計(jì)劃項(xiàng)目(吉市科計(jì)字[2012]32號(hào)9)

*李三華(1982-)，女，江西吉安人，講師，碩士，主要從事復(fù)分析研究(E-mail: lisanhua@sina.com);

吳高翔(1980-)，男，江西吉安人，講師，主要從事微分方程研究(E-mail: wugaoxiang_jgsu@163.com).