论文标题
关于广义高几何方程的连接问题
On a Connection Problem for the Generalized Hypergeometric Equation
论文作者
论文摘要
我们研究了奇异点的基本解决方案系统之间的连接问题$ 0 $和$ 1 $，用于广义超几何方程，该方程被广义超几何序列$ {} _ nf_ nf_ {n-1} $所满足。通常，$ x = 1 $的本地解决方案空间由一维单数解决方案空间和$ n-1 $尺寸全体形态解决方案空间组成。因此，在$ n \ ge3 $的情况下，连接矩阵的表达取决于$ x = 1 $的基本解决方案系统的选择。关于普通微分方程的连接问题，Schäfke和Schmidt（LNM 810，Springer，1980）给出了一个令人印象深刻的想法，重点是基本解决方案系统的系列扩展。我们应用他们的想法来解决广义高几何方程的连接问题并得出连接矩阵。
We study a connection problem between the fundamental systems of solutions at singular points $0$ and $1$ for the generalized hypergeometric equation which is satisfied by the generalized hypergeometric series ${}_nF_{n-1}$. In general, the local solution space around $x=1$ consists of one dimensional singular solution space and $n-1$ dimensional holomorphic solution space. Therefore in the case of $n\ge3$, the expression of connection matrix depends on the choice of the fundamental system of solutions at $x=1$. On the connection problem for ordinary differential equations, Schäfke and Schmidt (LNM 810, Springer, 1980) gave an impressive idea which focuses on the series expansion of fundamental system of solutions. We apply their idea to solve the connection problem for the generalized hypergeometric equation and derive the connection matrix.
