CANONICAL-FORMS OF DIFFERENTIAL-EQUATIONS FREE FROM ACCESSORY PARAMETERS

被引：13

作者：

HARAOKA, Y

机构：

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1994年 / 25卷 / 04期

关键词：

SYSTEMS OF OKUBO NORMAL FORM; ACCESSORY PARAMETERS; CHARACTERISTIC EXPONENTS; HYPERGEOMETRIC FUNCTIONS;

D O I：

10.1137/S0036141092231082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Systems of differential equations free from accessory parameters are defined and studied by Okubo [Seminar Reports of Tokyo Metropolitan University, 1987]. They are Fuchsian on the complex projective line, and there is an algorithm of determining monodromy representations for such systems. The Gauss hypergeometric equation, the generalized hypergeometric equation, the Pochhammer equation and a one-dimensional section of the Appell hypergeometric system F3 are known to be reduced to such systems. Recently Yokoyama classified all the systems of differential equations which are irreducible and free from accessory parameters in terms of multiplicities of characteristic exponents. This paper presents canonical forms of all such systems and will define a new class of special functions.

引用

页码：1203 / 1226

页数：24