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《Journal of Wuhan University(Natural Science Edition)》 1990-01
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A FORMULA OF SOLUTION FOR A KIND OF RECURRENCE RELATION WITH TWO PARAMETERS

Yu Chang'an (Department of Mathematics,Wuhan University)  
In this paper,the solution for a kind of recurrence relation with two parameters u_(ij)=∑~(p-2)_(λ=0)a_((p-1)-λ)u_((i-1-λ)_j)+a_0u_(i-n j-1)(i≥p-1+nj,j=0,1,…) u_(λ,0)=c_λ(λ=0,1,…,p-2),u_(i,j)=0(j0,or j≥1 and ip-1+nj,i=0,1…) (where p≥2,n≥0,a_k(k=0,1,…,p-1)and c_λ(λ=0,1,…p-2)are arbitrary constants)is given by an explicit formula u_(i·j)={∑~(p-2)_(λ=0){∑~λ_(k=0){F[(i-k-nj-(p-1)),j]}a_(λ+1-k)}c_λ}a_0~j (i=0,1,2,"",j=0,1,"",n≥0) This consequence is all of certain meaning in theory and practice.
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