常系数线性差分方程解的显式表示  

THE EXPLICIT REPRESENTATION OF SOLUTION OF LINEAR DIFFERENCE EQUATION WITH CONSTANT COEFFICIENTS

作　　者：蒋兴国[1] 季素月 

机构地区：[1]扬州大学农学院 [2]扬州师院数学系

出　　处：《扬州师院学报（自然科学版）》1994年第3期19-24,共6页

摘　　要：将n阶常系数线性差分方程x(t+n)=sum from i=1 to n(a_ix(t+n-i)+g(t))化为矩阵形式,进而求得它的解的显式表示,即表示为a_1(i=1,2,…,n)和g(t)的关系式,并使该解不涉及不定方程x_1+2x_2+…+nx_n-t求非负解问题;同时给出了一种新的用二项式系数表示Fibonacci数列解的关系式。This paper turns the n-th order linear difference equation with constant coefficients x(t+n)= sum from i=1 to n a_i x(t+n-i)+g(t) into the matrix form. Obtains the explicit representation of solution of the equation. As compared with the usual approach which invokes the nonnegative integer solutions of the linear Diophantine equation x_1+2x_2+…+nx_n=t, the formula given in this paper is explicily constructed via the use of a_i(i=1,2,…,n) and g(t). Obtains the solution of Fibonacci sequence, which is made up by binomial coefficients.

关 键 词：常系数 差分方程 解 显式表示 线性代数 

分 类 号：O151.2[理学—数学]