We present a closed-form solution for nth 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.
CITATION STYLE
Gonoskov, I. (2014). Closed-form solution of a general three-term recurrence relation. Advances in Difference Equations, 2014(1). https://doi.org/10.1186/1687-1847-2014-196
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