Abstract: The main purpose of this paper is to give some applications of a formula on the inversion of a linear differential polynomial obtained by the author in a previous work. One application concerns the proof of a theorem of Frank-Weissenborn and another application concerns an extension of a theorem of Hayman-Miles. As consequences of the results so obtained and theorems on linear differential equations, some other extensions of the theorems of Frank-Weissenborn and Hayman-Miles are also obtained.

Key words: inversion formula, theorems of Frank-Weissenborn and Hayman-Miles, linear differential equation

摘要： 在本文中利用关于线性微分多项式的一个反演公式和关于线性微分方程的一个定理，得出了Frank－Weissenborn 和 Hayman－Miles的几个定理的一些推广。

关键词: 反演公式, Frank－Weissenborn和Hayman－Miles的几个定理, 线性微分方程