On the difference equation xn = xn-k / (b + cxn-1...xn-k)

Abstract We describe the behavior of well-defined solutions of the difference equation x n = x n - k b + cx n - 1 ⋯ x n - k , n ∈ N 0 , where k ∈ N , parameters b , c and the initial values x − k , … ,  x −1 are real numbers. These results, among others, improve and extend our results in [S. Stevic, More on a rational recurrence relation, Appl. Math. E-Notes 4 (2004) 80–85].

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