涉及二阶线性递归序列的两类多项式的因式分解

The Decomposition of two Kinds of Polynomials Involving 2-order Linear Recursive Sequence

定义了与二阶线性递归序列{w_n}相关的序列{d_(i,j)}和{d_(i,j)},及与序列{w_n},{di,j}和{di,j}相关的多项式r_n(x),l_n(x),t_n(x)和t_n(x),根据{w_n}的递推关系和相关性质,研究了{d_(i,j)}和{d_(i,j)}的相关性质,得到了一系列关于l_n(x),t_n(x)和t_n(x)的多项式的因式分解.

In this paper,new sequences{ d_（i,j）} and{d_（i,j）},and their related 2-order linear recursive sequence{ w_n} were defined,and some polynomials r_n（x）,l_n（ x）,t_n（ x） and t_n（ x） associated with { w_n},{ d_（i,j）} and{d_（i,j）} were defined. According to the recurrence relation and related properties of sequence{ wn} and we studied the properties of { d_（i,j）} and{d_（i,j）},a series of l_n（ x）,t_n（ x） and t_n（ x） polynomial factorization were obtained.