| 摘要: |
| 本文研究了整函数及其线性微分多项式的高阶导数分担一个非零有穷复数的唯一性问题.利用正规族理论改进并推广了Goutam Kumar Ghosh的结果，证明了一个唯一性定理：设f为非常数整函数,α是非零有穷复数,m≥0是整数.若f=a⇒f'=a,f'=a ⇒ L (m)=L(m+1)=a,则f≡L=βez或f=a+βez，其中β(≠0)是常数. |
| 关键词: 唯一性 正规族 整函数 线性微分多项式 |
| DOI： |
| 分类号:O174.52 |
| 基金项目:国家自然科学基金资助(11871216). |
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| UNIQUENESS OF ENTIRE FUNCTIONS INVOLVING LINEAR DIFFERENTIAL POLYNOMIALS |
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LIU Ban-yan, LIU Xiao-jun
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College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
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| Abstract: |
| This paper studies the uniqueness problem of entire functions and the higher order derivatives of their linear differential polynomials sharing one finite non-zero value. By using the theory of normal families, the results of Goutam Kumar Ghosh are improved and generalized, and a uniqueness theorem is proved: Let f be a nonconstant entire function, a be a non-zero complex number, and m ≥ 0 be an integer. If f=a⇒f'=a, and f'=a ⇒ L (m)=L(m+1)=a, then f≡L=βez or f=a+βe2, where β(≠0) is a constant. |
| Key words: uniqueness normal family entire function linear differential polynomial |
