用无限阶矩阵求微分方程在奇点处的级数解

Series Solutions of Linear Ordinary Differential Equation at Singular Point by Infinite Order Matrix

LI Dalin¹,², LV Xianrui¹

1. Institute of Mathematics, Jilin University, Changchun 130012, China; 2. Department of Foundation,Liuzhou Vocational Institute of Technology, Liuzhou 545006, Guangxi Zhuang Autonomous Region, China

Received:2006-06-26 Revised:1900-01-01 Online:2007-03-26 Published:2007-03-26
Contact: LV Xianrui

Abstract

Abstract: The series solutions of the linear ordinary differential equation at singular point were studied via the infinite order matrix of the linear differential operator in power series basis. We got a recurrence formula to compute the characteristic vectors of the infinite order matrix belonging to λ=0 and then completed the expression of the series solutions with the characteristic vectors. The regularity of singular point is judged with a finite order matrix, and the Fuchs theorem has been improved.

Key words: ordinary differential equation, infinite order matrix, characteristic vector, series solution, regular singular point

CLC Number:

O175.1

LI Dalin,, LV Xianrui. Series Solutions of Linear Ordinary Differential Equation at Singular Point by Infinite Order Matrix[J].J4, 2007, 45(02): 203-207.

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Series Solutions of Linear Ordinary Differential Equation at Singular Point by Infinite Order Matrix

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