On the Convergence of a Formal Solution to an Ordinary Differential Equation

被引：4

作者：

Bruno, A. D. ^{[1
]}

Goryuchkina, I. V. ^{[1
]}

机构：

[1] Russian Acad Sci, MV Keldysh Appl Math Inst, Moscow 125047, Russia

来源：

DOKLADY MATHEMATICS | 2010年 / 81卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Formal Solution; DOKLADY Mathematic; Coeffi Cients; Linear Differential Operator; Integer Power;

D O I：

10.1134/S1064562410030063

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A theorem on the convergence of a power series with integer power exponents that is a formal solution to an nth-order ordinary differential equation has been reported. The maximum order of the derivative in the differential sum f (x, z) is called its order of differentiation and is denoted by π( f ). The power exponents can be made arbitrarily large by increasing the initial part of solution expansion.

引用

页码：358 / 361

页数：4

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