Closed-form solution of a general three-term recurrence relation

Advances in Difference Equations

Ivan Gonoskov¹ 

[1] Department of Physics, Umeå University, Umeå, Sweden

关键词: Exact Solution;    Recurrence Relation;    Index Number;    Global Index;    Elementary Operation;   

DOI  :  10.1186/1687-1847-2014-196

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We present a closed-form solution for n th term of a general three-term recurrence relation with arbitrary given n-dependent coefficients. The derivation and corresponding proof are based on two approaches, which we develop and describe in detail. First, the recursive-sum theory, which gives the exact solution in a compact finite form using a recursive indexing. Second, the discrete dimensional-convolution procedure, which transforms the solution to the non-recursive expression of n, including a finite number of elementary operations and functions.

【 授权许可】

CC BY