特殊行列式D_n(m,k)的计算

Computation of a Specific Determinant D_n(m,k)

给出了计算以数列 {Pn}的项为元素的特殊行列式 Dn( m,k)的一般公式 .以及数列 {Pn}一般项由递推公式 Pn+ 1( x) =s( x) Pn( x) + t( x) Pn-1( x)确定时 ,求数列一般项的公式 ,并讨论了当 Pn=ncλn + P0 λn( c,λ,P0 为常数 )且 m <n - 1时 ,Dn( m,k) =0的重要性质 ,最后指出 Fibonacci,chebyshev行列式的计算 。

The general formula is given for calculating the specific determinant, whose elements are the terms of a number sequence ｛P n｝. The formula is also given for calculating the terms when the terms are determined by the recursion formula of P n+1 (x)=S(x)+P n-1 (x)·t(x). The important characteristics of D n(m,k)=0 were discussed when P n=ncλ n+P oλ n(c,λ,P o are all constants) and m<n-1.It is pointed that Fibonacci's and chebyshev's determinants are two specific examples of the proposition.