超几何方程的一类非齐次边值问题解的相似结构

Similar Structure of Solution for a Class of Non-Homogeneous Boundary Value Problems of Hypergeometric Equation

摘要: 本文对超几何方程的一类非齐次边值问题的解做了深入分析，发现可以通过构造引解函数和左、右相似核函数，得到解的相似结构式，并提出求解相似结构式的相似构造法。对一个具体的超几何方程边值问题的求解进一步说明：相较于传统的求解步骤，运用相似构造法求解边值问题更加快速便捷；解的相似结构式表示为连分式乘积，不仅体现了解的形式美，更反映出定解方程的解与边界条件系数之间的相互联系。

Abstract: In this paper, the solution of a class of nonhomogeneous boundary value problems for hypergeometric equation is studied in detail. It is founded that the solution’s similar structure formula can be obtained by constructing the derivation function, the left similar kernel function and the right similar kernel function; and then, a similar construction method for solving the similar structure formula is proposed. A solution of boundary value problem to a specific hypergeometric equation further explained that comparing with the traditional solution steps, it is more convenient and faster to solve boundary by using the similar construction method. Further, the similar structure formula of solution is expressed as the product of continued fraction, which not only shows the formal beauty of the solution, but also reflects the interrelation between the solution of the definite solution equation and the boundary condition coefficient.