導數(shù)分擔三個值的亞純函數(shù)的唯一性

邱凎俤

(寧德師范學院數(shù)學系,福建寧德 352100)

導數(shù)分擔三個值的亞純函數(shù)的唯一性

邱凎俤

(寧德師范學院數(shù)學系,福建寧德 352100)

主要討論兩個亞純函數(shù)的k階導數(shù)分擔三個值時的唯一性問題,并得到一個有趣的結(jié)果.

亞純函數(shù);分擔值;唯一性

1 引言及主要結(jié)果

本文采用亞純函數(shù)的Nevanlinna理論的標準記號[1],S(r,f)表示任意滿足

2 幾個引理

3 定理1的證明

將F與G的公共a-值點代入上式便得c=a,即有h=a.由情況1的討論知又產(chǎn)生矛盾.

定理1得證.

[1]Hayman W K.Meromorphic Functions[M].Oxford:Clarendon Press,1964.

[2]儀洪勛,楊重駿.亞純函數(shù)惟一性理論[M].北京:科學出版社,1995.

[3]Li P.Meromorphic functions that share four small functions[J].J.Math.Anal.Appl.,2001,263:316-326.

[4]Qiu G D.Meromorphic functions whose derivatives share four small functions[J].Indian J.of Pure and Applied Math.,2002,33:761-767.

Meromorphic functions that share three values

Qiu Gandi

(Department of Mathematics,Ningde Normal University,Fujian352100,China)

In this paper,we mainly discussed the uniqueness problem of meromorphic functions whose their derivatives that share three values and obtained a interesting result.

meromorphic functions,sharing value,uniqueness

O174.52

A

1008-5513(2013)03-0226-07

10.3969/j.issn.1008-5513.2013.03.002

2011-04-10.

福建省高校科研項目(JK2010062);福建省自然科學基金(S0750013);福建省教育廳A類科技項目(JA11276).

邱凎俤(1955-),教授,研究方向：復分析及其應用.

2010 MSC:30D35