摘要
本文以更加清楚的形式推广了文献[1]的结果,得到了一般三项非齐次递推式的一般解方法,从而摆脱了求解高阶代数方程的所有根的困难。
In this paper, the following result is obtained.Theorem General solutions of the general non-homogeneous trinomial recurrences α_(n+p)=α_(r_1)α_(n+r_1)+α_(r_0)α_(n+r_0)+β_λ α_i=c_i (i=0,1,…,p-1)(where n≥0,p>r_1>r_0≥0; α_(r_1),α_(r_0) and β_λ(λ=0,1,…)are constants)are given by thefollowing formuls U_(n+p)=sub from j=0 to 1(sub from i=r_j to p-1 (A^(n-i+r_j)(r_0,r_1)c_i)α_(r_j))+sub from λ=0 to n A^(n-λ)(r_0, r_1)β_λHere n, λ=0,1,…,but A^(n)(r_0,r_1)=∑ (p-r_0)b_(r_0)+(p-r_1)b_(r_1)=n^(b_(r_0)+b_(r_1) b_(r_0))α_(r_0)~b(r_0)α_(r_1)b_(r_1) when n≥0 0 when n<0
关键词
递推式
二元一次
不定方程
初始值
recurrences
indefinite binary equation of the first degree
initial value
