Abstract

In this paper, we propose a package for symbolic construction of exponential–logarithmic solutions to linear differential equations whose coefficients are represented in incomplete form, i.e., as power series for which only a finite number of initial terms is known. The series involved in the solutions are also represented in incomplete form. For each such series, the maximum possible number of initial terms is constructed, which are uniquely determined by known terms of coefficients of a given equation. Additionally, the truncation degree of each series in a solution should not exceed a value specified by the user. It ensures the termination of the computation even when any number of the terms of the series involved in the solution can be defined by known terms of the coefficients of a given equation.

中文翻译：

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系数作用下具有无限和截断幂级数的线性微分方程截断解的构造程序。

摘要

在本文中，我们为线性微分方程的指数对数解的符号构造提出了一个程序包，该线性微分方程的系数以不完整的形式表示，即作为幂级数，其初始项有限。解决方案中涉及的系列也以不完整的形式表示。对于每个这样的序列，构造初始项的最大可能数目，其由给定方程式的系数的已知项唯一地确定。此外，解决方案中每个系列的截断度不应超过用户指定的值。即使可以通过给定方程式的系数的已知项定义解决方案中涉及的序列中的任何数量的项，也可以确保计算的终止。