反正就是说齐次差分方程就是那个式子的形式了。
接着466页上讲到
Theorem. let the polynomial
Ψ(u) = u^r + a(r-1)u^(r-1) + ... + a(0)
have the k distinct zeros λ(i) ,i = 1,2,...,k
with multiplicities σ(i),i = 1,2,...,k
and let a(0) != 0,then for arbitray polynomials p(i)(t) with deg p(i) < σ(i),i = 1...k;
the sequence
u(j) = p(1)(j)λ(1)^(j) + p(2)(j)λ(2)^(j) +...+ p(k)(j)λ(k)^(j)
is a solution of the difference eqution (7.2.9.1).Conversely,every solution of
(7.2.9.1)can be uniquely represented in the form(7.2.9.9).