Abstract

The approach we used earlier to construct Laurent and regular solutions enables one, in combination with the well-known Newton polygon algorithm, to find formal exponential-logarithmic solutions of linear ordinary differential equations the coefficients of which have the form of truncated power series. (Thus, only incomplete information about the original equation is available.) The series involved in the solution are also represented in truncated form. For these series, the combined approach proposed enables one to obtain the maximum possible number of terms.

中文翻译：

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线性常微分方程的截断级数和形式指数对数解

摘要

我们之前用来构造Laurent的方法和正则解使人们能够与著名的Newton多边形算法结合起来，找到线性常微分方程的形式指数对数解，其系数具有截断幂级数的形式。（因此，仅提供有关原始方程式的不完整信息。）解决方案中涉及的级数也以截短形式表示。对于这些系列，所提出的组合方法使人们可以获得最大可能的项数。