Closed-Form Solution of a Rational Difference Equation

Abstract

In this paper, we study the solution of the difference equation ${\mathrm{\Omega }}_{m+1}=\left({\mathrm{\Omega }}_{m-\left(7q+6\right)}/\left(1+{\displaystyle {\prod }_{t=0}^5{\mathrm{\Omega }}_{m-\left(q+1\right)t-q}}\right)\right)$ , where the initials are positive real numbers.