一般三项非齐次递推式的一般解方法

来源期刊：中南大学学报(自然科学版)1993年第1期

论文作者：殷志云

文章页码：117 - 121

关键词：递推式; 二元一次不定方程; 初始值

Key words：recurrences; indefinite binary equation of the first degree; initial value

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。

Abstract: In this paper, the following result is obtained.Theorem General solutions of the general non-homogeneous trinomial recurrences α_n+p=α_r1α_n+r1+α_r0α_n+r0+β_λ α_i=c_i (i=0,1,…,p-1)(where n≥0,p>r₁>r₀≥0; α_r1,α_r0 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(r₀,r₁)c_i)α_rj)+sub from λ=0 to n A^n-λ(r₀, r₁)β_λHere n, λ=0,1,…,but Aⁿ(r₀,r₁)=∑ (p-r₀)b_r0+(p-r₁)b_r1=n^b_r0^+b_r1 ^b_r0α_r0^b(r₀)α_r1b_r1 when n≥0 0 when n<0