| 吴昭君.无限级整函数在角域内的取值和增长性[J].数学年刊A辑,2015,36(1):81~90 |
| 无限级整函数在角域内的取值和增长性 |
| Growth and Values of the Infinite Order Entire Function in an Angular Domain |
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| DOI： |
| 中文关键词: 熊氏无限级, 径向振荡, 值分布 |
| 英文关键词:Hiong's infinite order, Radial oscillation,
Value distribution |
| 基金项目:本文受到国家自然科学基金 (No.11201395) 的资助. |
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| 中文摘要: |
| 借助熊庆来的无限级, 将Nevanlinna建立的有限级整函数在角域内的取值和增长性
的结果推广到无限级. 作为应用, 研究了高阶超越整函数系数微分方程$f^{(k)}+A_{k-2}(z)f^{(k-2)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0$
解的径向振荡. |
| 英文摘要: |
| By using Hiong's infinite order, the author extends a classical result due to Nevanlinna on
the growth and values of the finite order entire function in an angular domain to the infinite order.
As an application, the radial oscillation of the solutions of the higher order homogeneous linear differential equation
$$f^{(k)}+A_{k-2}(z)f^{(k-2)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0$$
with transcendental entire function coefficients is studied. |
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