欧拉超几何方程边值问题的解的相似结构

The Similar Structure of Solutions for the Boundary Value Problem of Euler’s Hypergeometric Differential Equation

利用微分方程在无穷大处的两个基本解,讨论了欧拉超几何微分方程边值问题的解的相似结构,确定了解的相似核函数.欧拉超几何微分方程的边值问题的解具有统一的相似结构式,且仅由左边界条件唯一确定.对于右边界条件的改变,只需改变其相似核,就可以得到边值问题的相似结构式.解的相似结构式的获得,有利于进一步分析解的内在规律.

Using the two basic solutions on the infinite of differential equation, discussed the similar structure of the solutions of the Euler[s hypergeometric differential equation, and defined the similar kernel function of the solutions. It confirmed that the solutions for the boundary value problem of Euler^s hyper- geometric differential equation have the unifor expression,it determined uniquely by the left boundary con- dition only. About changed the right boundary condition,it can obtain the similar structure of the boundary value problem only by changed its similar kernel function. The similar structure of solution is attained in this paper,which is beneficial to understand the inherent laws of analytic soution.