Truncated and Infinite Power Series in the Role of Coefficients of Linear Ordinary Differential Equations

机译：截断和无限功率系列中的线性常微分方程系数的作用

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We consider linear ordinary differential equations, each of the coefficients of which is either an algorithmically represented power series, or a truncated power series. We discuss the question of what can be learned from equations given in this way about its Laurent solutions, i.e., solutions belonging to the field of formal Laurent series. We are interested in the information about these solutions, that is invariant with respect to possible prolongations of the truncated series which are the coefficients of the given equation.

机译：我们考虑线性常微分方程，其每个系数是算法上表示的功率系列或截断的功率系列。我们讨论了以这种方式可以从这种方式学习的问题，即其劳伦语解决方案，即属于正式劳伦斯系列领域的解决方案。我们对这些解决方案的信息感兴趣，这对于截断系列的可能延长是不变的，这是给定等式的系数的截断。

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《International Workshop on Computer Algebra in Scientific Computing》|2020年|63-76|共14页
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Sergei A. Abramov; Denis E. Khmelnov; Anna A. Ryabenko;
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Differential equations; Truncated power series; Algorithmically represented infinite power series; Laurent series; Computer algebra systems;

机译：微分方程;截短的电源系列;算法表示的无限功率系列;Laurent系列;计算机代数系统;

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1. A symbolic algorithm for exact power series solutions of nth order linear homogeneous differential equations with polynomial coefficients near an ordinary point [J] . Kiymaz O Applied mathematics and computation . 2006,第2期

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2. Procedures for Searching Laurent and Regular Solutions of Linear Differential Equations with the Coefficients in the Form of Truncated Power Series [J] . Abramov S. A., Ryabenko A. A., Khmelnov D. E. Programming and Computer Software . 2020,第2期

机译：在截断功率系列形式中搜索Laurent和线性微分方程的常规解的程序
3. Exponential function method for solving nonlinear ordinary differential equations with constant coefficients on a semi-infinite domain [J] . Ali Hatam, Edmund Chadwick, Saeed Kazem Proceedings of the Indian Academy of Sciences. Mathematical sciences . 2016,第1期

机译：半无限域上具有常系数的非线性常微分方程的指数函数方法
4. Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems [C] . Sergei A. Abramov, Moulay A. Barkatou International workshop on computer algebra in scientific computing . 2014

机译：线性微分系统系数作用下的可计算无限次幂级数
5. Comparison and Spectral Theory for Ordinary Differential Equations with Distributional Coefficients [D] . Ghatasheh, Ahmed A. 2018

机译：分布系数的常微分方程的比较与光谱理论
6. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients [O] . Vyacheslav M. Boyko, Roman O. Popovych, Nataliya M. Shapoval -1

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7. Linear Ordinary Differential Equations with Gevrey Coefficients(Generalized Functions and Linear Differential Equations, VIII) [O] . Komatsu Hikosaburo 1983

机译：具有Gevrey系数的线性常微分方程（广义函数和线性微分方程，VIII）
8. Solution of Ordinary Differential Equations Using Power Series with Decomposed Coefficients. Part 1. Mathematical Analysis [R] . Schett, A., Collin, M., Perrier, R. 1985

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Truncated and Infinite Power Series in the Role of Coefficients of Linear Ordinary Differential Equations

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