| 摘要: |
| 本文基于正规族理论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, 改进了 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, a 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=βe^(z) 或 f=a+βe^(z), 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:国家自然科学基金项目（11871216） |
|
| uniqueness of entire functions involving linear differential polynomials |
|
liu banyan, liu xiaojun
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| Abstract: |
| Based on the theory of normal families, 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. It improves the results of Goutam Kumar Ghosh and establishes a uniqueness theorem: 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=βe^(z) or f=a+βe^(z), where β(≠ 0) is a constant. |
| Key words: uniqueness normal family entire function linear differential polynomial |
