求解复合超几何微分方程边值问题解的一种新方法

A New Method for Solving the Boundary Value Problem of Compound Hypergeometric Differential Equation

摘要: 针对复合超几何微分方程的边值问题，研究其求解过程并分析解的结构，发现：首先利用左、右区超几何方程的任意一组线性无关的解构造引解函数，然后利用右区引解函数和右边值条件的系数构造右相似核函数，左区引解函数和交界处衔接条件的系数构造左相似核函数，最后将左相似核函数与左边值条件的系数组合得到该边值问题解的相似结构，并总结出求解该类边值问题的相似构造法。

Abstract: In the boundary value problem of the compound hypergeometric differential equation, first of all, the leading function is constructed by any two linearly independent solutions of the definite solution equation in the left and right regions. Then, right similar kernel function is obtained through leading function and coefficients of the boundary condition in right area. Furthermore, with the combination of leading function in left area and coefficients of junction conditions, left similar kernel function can also get. Finally, combining left similar kernel function with coefficients of the boundary condition in left area, it is easy to get a similar structure of the solutions in this boundary value problem. Overall, we conclude that a new method to solve this kind of boundary value problem. It is called similar construction method.