论文标题
在高斯超几何方程的汇合处出现的stokes现象
Stokes phenomenon arising in the confluence of the Gauss hypergeometric equation
论文作者
论文摘要
在本文中，我们深入研究了高斯和Kummer高几何方程。特别是，我们专注于高斯超几何方程的两个常规奇异性的汇合，以产生kummer超几何方程，而无穷大。我们展示了如何从磁盘中分析的能量行为的解决方案传递到具有指数行为的解决方案，这些解决方案是在扇区中进行分析并且具有不同渐近性的解决方案。我们明确地根据围绕合并奇异性的原始系统的单构型数据（特别是连接矩阵）来明确计算汇合系统的Stokes矩阵。
In this paper we study the Gauss and Kummer hypergeometric equations in depth. In particular, we focus on the confluence of two regular singularities of the Gauss hypergeometric equation to produce the Kummer hypergeometric equation with an irregular singularity at infinity. We show how to pass from solutions with power-like behaviour which are analytic in disks, to solutions with exponential behaviour which are analytic in sectors and have divergent asymptotics. We explicitly calculate the Stokes matrices of the confluent system in terms of the monodromy data, specifically the connection matrices, of the original system around the merging singularities.
