论文标题
对3个变量和普通微分方程的紫红色系统的研究，作为其限制
A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions
论文作者
论文摘要
提出了3个带有4个参数的3个变量中的等级8的紫红色系统。奇异基因座由六个平面和一个立方体组成。该系统限制到两个单数平面的交点是一个普通的微分方程，该方程是四个单数点的四个订单。该方程式的中间卷积证明是两个高斯高几何方程的张量产物，另一个中间卷积将此方程发送到dotsenko-fateev方程。找到了这些普通微分方程的局部解决方案。它们的系数是伽马功能的产物总和。这些总和可以表示为1 $ _4f_3 $在1的特殊值。 关键字：紫色微分方程，超几何微分方程，中间卷积，dotsenko-fateev方程，复发公式，串联解决方案
A Fuchsian system of rank 8 in 3 variables with 4 parameters is presented. The singular locus consists of six planes and a cubic surface. The restriction of the system onto the intersection of two singular planes is an ordinary differential equation of order four with three singular points. A middle convolution of this equation turns out to be the tensor product of two Gauss hypergeometric equation, and another middle convolution sends this equation to the Dotsenko-Fateev equation. Local solutions to these ordinary differential equations are found. Their coefficients are sums of products of the Gamma functions. These sums can be expressed as special values of the generalized hypergeometric series $_4F_3$ at 1. Keywords: Fuchsian differential equation, hypergeometric differential equation, middle convolution, Dotsenko-Fateev equation, recurrence formula, series solution
