2017
Том 69
№ 9

All Issues

A Note on the Recursive Sequence $x_{n + 1} = p_kx_n + p_{k − 1}x_{n − 1} +...+ p_1x_{n − k + 1}$

Stevic S.

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Abstract

We present some comments on the behavior of solutions of the difference equation $x_{n + 1} = p_kx_n + p_{k − 1}x_{n − 1} +...+ p_1x_{n − k + 1}$, $n = −1, 0, 1,…,$ where $p_i ≥ 0, i = 1,..., k, k ∈ N$, and $x_{−k},..., x_{−1} ∈ R$.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 4, pp 691–697.

Citation Example: Stevic S. A Note on the Recursive Sequence $x_{n + 1} = p_kx_n + p_{k − 1}x_{n − 1} +...+ p_1x_{n − k + 1}$ // Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 570-574.

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