Canonical forms of differential equations free from accessory parameters
Canonical forms of differential equations free from accessory parameters
复制标题
没有附加参数的微分方程的规范形式
DOI：
10.1137/s0036141092231082
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发表时间：
1994
影响因子：
2
通讯作者：
Y. Haraoka
中科院分区：
文献类型：
--
作者：
Y. Haraoka
大久保定义和研究了不含附加参数的微分方程组[东京市立大学研讨会报告，1987]。它们在复射影线上是富克斯的，并且有一种算法来确定这类系统的单行表示。已知的高斯超几何方程、广义超几何方程、波希哈默尔方程和Appell超几何系统的一维截面F_3都可归结为此类系统。最近，横山利用特征指数的重数对所有不可约且不含附加参数的微分方程组进行了分类。本文给出了所有这类系统的规范形式，并将定义一类新的特殊函数。
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 $F_3 $ 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.