关于Frank－Weissenborn和Hayman－Miles的几个定理

On Theorems of Frank-Weissenbornand Hayman-Miles

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。

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