n阶变系数线性差分方程的解

本文利用变数算符￣［２］以及给出变数算符和移动算符的乘积关系，并定义变系数移动算符幂级数间的乘积且证明其在Ｍｉｋｕｉｕｓｋｉ收敛意义下是正确的；另外，把一般的ｎ阶变系数线性差分方程转化为一个恰当的算符方程组，从而获得一般ｎ阶变系数线性差分方程的解。

Solutions of the General n-th Order Variable Coefficients Linear Difference Equation

In this paper, variable operator and its product with shifting operator are studied. Similar to the classical power series, the product of power series of shifting operator with variable coefficient is defined and its convergence is proved under Mikusinski's sequence convergence. Furthermore, with a general variable coefficient linear difference equation of the n-th order which is turned into a set of operator equations, we can obtain the solutions of the general n-th order variable coefficient linear difference equation.