On the Recursive Sequence $x_{n+1} = \frac{x_{n-2k-3}}{1 + \prod\limits_{m=1}^{k+1} x_{n-2m+1}}$: In memoriam Professor Charles E. Chidume (1947–2021)

Piyanut Puangjumpa

On the Recursive Sequence $x_{n+1} = \frac{x_{n-2k-3}}{1 + \prod\limits_{m=1}^{k+1} x_{n-2m+1}}$

In memoriam Professor Charles E. Chidume (1947–2021)

Authors

Piyanut Puangjumpa Surindra Rajabhat University

Keywords:

difference equation, period 2k+4 solution, recursive sequence

Abstract

In this paper, a solution of the following difference equation was investigated
$$x_{n+1} = \frac{x_{n-2k-3}}{1 + \prod\limits_{m=1}^{k+1}x_{n-2m+1}}, n = 0, 1, 2, \ldots$$
where $x_{-2k-3}, x_{-2k-2}, \ldots, x_{-1}, x_{0}$ are arbitrary positive real numbers and $k = 0, 1, 2, \ldots$.

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Published

2023-09-30

How to Cite

Puangjumpa, P. (2023). On the Recursive Sequence $x_{n+1} = \frac{x_{n-2k-3}}{1 + \prod\limits_{m=1}^{k+1} x_{n-2m+1}}$: In memoriam Professor Charles E. Chidume (1947–2021). Thai Journal of Mathematics, 21(3), 529–536. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1524