| 具有极点型奇点的二阶线性方程与广义解 |
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| 引用本文： | 马巧云,刘同生,何众琦. 具有极点型奇点的二阶线性方程与广义解[J]. 河南科学, 2011, 29(10): 1140-1144 |
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| 作者姓名： | 马巧云 刘同生 何众琦 |
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| 作者单位： | 1. 河南农业大学信息与管理科学学院,郑州,450002
2. 平顶山学院,河南平顶山,467002 |
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| 基金项目： | 河南省教育厅自然科学研究计划项目(2010A120004) |
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| 摘 要： | 给出二阶线性方程二阶极点邻域的级数形式解.传统观念认为适合方程的收敛级数才是方程的解.在这种观念的支配下,一些简单情形求得的发散级数形式上使方程成为恒等式,被称为解的渐近展开.发散级数适合方程并非个别现象.这个事实促使我们改变观念,承认使方程成为恒等式的发散级数是方程的(广义).
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| 关 键 词： | 变系数二阶线性方程 合成解法 发散级数 广义解 |
The Second Order Linear Equations with Pole and Generalized Solutions |
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| Ma Qiaoyun,Liu Tongsheng,He Zhongqi. The Second Order Linear Equations with Pole and Generalized Solutions[J]. Henan Science, 2011, 29(10): 1140-1144 |
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| Authors: | Ma Qiaoyun Liu Tongsheng He Zhongqi |
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| Affiliation: | Ma Qiaoyun 1,Liu Tongsheng 1,He Zhongqi 2 (1.College of Information and Management Science,Henan Agriculture University,Zhengzhou 450002,China,2.Pingdingshan University,Pingdingshan 467002,Henan China) |
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| Abstract: | The solutions of the neighborhood of the pole of second order linear equations are given.Traditional sense consider that converge series is solution.So the divergent series that suit the second order linear equayion is named asymptotic expansions.That divergent series suit the equation are more and more,this fact make a change in traditional sense.The divergent series that suit the second order linear equation is(generalized)solution were considered. |
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| Keywords: | second order linear equation with pole composition divergent series generalized solution |
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