用升阶法求常系数非齐次线性递推关系的特解

Special Solutions of Constant Coefficient Inhomogeneous Linear Recursion Relation with Rising Order

利用数列的差分算子和移位算子,将常系数非齐次线性递推关系转化成为常系数非齐次线性差分方程(q0△k+i+q1△k+i-1+…+qk△i)an=△if(n),并将f(n)=gm(n),f(n)=qngm(n),f(n)=qngm(n)cosβn,f(n)=qngm(n)sinβn)这四种类型的常系数非齐次递推关系转化为相应的差分方程,从而得到求常系数非齐次线性递推关系特解的简易方法——升阶法。

This article makes use of the sequence difference, and transforms the invariable coefficient number of times different linear recursion sequence to the coefficient inhomogeneous linear difference equation （ qo （qo△k＋i＋q1△k＋i-1…＋qk△i）an=△if（n）, The fourf（n）=gm（n）,f（n）=qngm（n）,f（n）=qngm（n）cosβn,f（n）=qkgm（n）sinβn） are discussed under constant coefficient inho-mogeneous linear difference equation, thus obtains the special solutions of coefficient inhomogeneous linear recursion sequence, which is called the method of increasing order.