论文标题
$ f'' + p（z）f = 0 $的渐近整合理论
Asymptotic integration theory for $f'' + P(z)f = 0$
论文作者
论文摘要
渐近整合理论给出了结果的集合，该理论对（*）$ f''+p（z）f = 〜0 $的渐近生长和零分布提供了详尽的描述，其中$ p（z）$是多项式。这些结果已被几位作者使用（*）解决方案的有趣属性。话虽如此，许多人指出，例如，在E.〜Hille的1969年书中\ Emph {关于普通微分方程的讲座}的证明和讨论很难遵循。本文的主要目的是通过对用于证明理论的推理并写出结果的完整而清晰的陈述，使该理论更容易理解和访问。材料的演示和解释的相当一部分与Hille的书不同。
Asymptotic integration theory gives a collection of results which provide a thorough description of the asymptotic growth and zero distribution of solutions of (*) $f''+P(z)f=~0$, where $P(z)$ is a polynomial. These results have been used by several authors to find interesting properties of solutions of (*). That said, many people have remarked that the proofs and discussion concerning asymptotic integration theory that are, for example, in E.~Hille's 1969 book \emph{Lectures on Ordinary Differential Equations} are difficult to follow. The main purpose of this paper is to make this theory more understandable and accessible by giving complete explanations of the reasoning used to prove the theory and by writing full and clear statements of the results. A considerable part of the presentation and explanation of the material is different from that in Hille's book.
