高斯超几何方程汇流中的斯托克斯现象
Stokes phenomenon arising in the confluence of the Gauss hypergeometric equation
摘要：
本文深入研究了Gauss和Kummer超几何方程。特别地，我们专注于高斯超几何方程的两个正则奇点的汇合，以产生在无穷远处具有不规则奇点的Kummer超几何方程。我们将展示如何通过从解决方案的权力一样的行为是解析的磁盘，解决方案的指数行为是解析的部门，并有发散渐近。我们明确计算的Stokes矩阵的合流系统的monodromy数据，特别是连接矩阵，周围的合并奇点的原始系统。
英文摘要：
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.
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