研究了一类高阶齐次线性微分方程解的零点收敛指数,并得到当方程的系数 A0 为整函数, 其泰勒展式为缺项级数, 并且A0 起控制作用时, 方程
f(k)+Ak-2f(k-2)+…+A1f′+A0f=0
的任意两个线性无关解 f1, f2 满足 max{λ(f1),λ(f2)}=∞,其中 λ(f) 表示亚纯函数 f的零点收敛指数.
Abstract
We investigate the exponent of convergence of zeros of solutions for some higher order homogeneous linear differential equation. When A0 is an entire function that its taylor expansion is a gap power series and A0 is the dominant coefficient, we proved that any two linearly independent solutions f1 and f2 of equation
f(k)+Ak-2f(k-2)+…+A1f′+A0f=0
satisfy max{λ(f1),λ(f2)}=∞, where λ(f) denotes the exponent of convergence of zeros of meromorphic function f.
关键词
微分方程 /
零点收敛指数 /
缺项级数
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Key words
differential equation /
exponent of convergence of zeros /
gap power series
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参考文献
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脚注
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基金
国家自然科学基金资助项目 (11171119)
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