关于常系数线性非齐次递推关系的求解

Solution to the Linear Nonhomogeneous Recursive Relation with Constant Coefficients

本文利用构造生成函数的方法给出常系数线性非齐次递推关系 :h(n) =a1h(n- 1) +… +akh(n -k) +f(n)解的一般公式及其应用 ,其中f(x)为一般函数。本文的方法是对文献 [1][2 ]中特殊形式f(x) =βnPl(n)求解的一种推广 。

In this paper, we give a general solution to the linear nonhomogeneous recursive relation with constant coefficients and its application. This method is an extension of special form f（x） =β^nP1（ n ） in reference[ 1 ] [ 2] and of more generality.