On the difference equation x n+1 = x nx n-k/ (x n-k+1 (a + bx nx n-k))

Abstract

We show that the difference equation x n+1 = x nx n-k / (x n-k+1 (a + bx nx n-k)), n ∈ 0, where k ∈ , the parameters a, b and initial values x - i, i = 0, k are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior of well-defined solutions of the equation.