关于双指标三项线性递推式的一般解

A General Solution for Trinomial Linear Recurrence with two Indices

该文给出了一类双指标的三项线性递推式的一般解公式．有关结论，对具大数值双指标的相应速推式的解的求出，或在有关理论的研究方面，都有其作用．

In this paper we consider the following trinomial linear recurrence with two indicis Ui,j = f(i,j)Ui,j-p+ g(i,j)Ui-1,j-p + h(i,j) , U1,s = Cs(s = 1,2,..,p) ,Ui,j = 0 (i<1 or j < 1 or j ≤ q(i - 1)),where i,j = l , 2, ... ;p,q ≥ 1 ;f(i,j),g(i,j) and h(i,j) are variable numbers ; c,(s = 1 , 2,.., p) are constant numbers. Its general solution is given by the formulaUi,j = { F(i,j ;i - 1, θ1, 1 ) } C(j-q(i-1)-pθ1)