New class of practically solvable systems of difference equations of hyperbolic-cotangent-type

Abstract

The systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$, $s_n$ are $x_n$ or $y_n$, are studied. It is shown that each of these sixteen systems is practically solvable, complementing some recent results on solvability of related systems of difference equations.

Keywords

• system of difference equations
• general solution
• solvability of difference equations
• hyperbolic-cotangent-type system of difference equations