On the Difference Equation xn+1=xnxn-k/(xn-k+1a+bxnxn-k)

Abstract

We show that the difference equation xn+1=xnxn-k/xn-k+1(a+bxnxn-k),n∈ℕ0, where k∈ℕ, the parameters a, b and initial values x-i, i=0,k̅ 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.