A Solution Form of a Rational Difference Equation

Abstract

This paper shows the solution form of the rational difference equation \begin{equation*} x_{n+1}=\frac{ax_{n-(2k+3)}}{-a\mp x_{n-(k+1)}x_{n-(2k+3)}}\text{ }% ,~n=0,1,... \end{equation*} where $k$ is a positive integer $a$ and initial conditions are non-zero real numbers with $x_{n-(k+1)}x_{n-(2k+3)}\neq \mp a$ for all $n\in N_{0}$.