On difference Riccati equations and second order linear difference equations (Q633256)

The author considers second order linear difference equations and the associated difference Riccati equation in the complex domain, namely \[ \Delta^2y(z) + A(z)y(z)=0 \] and \[ \Delta f(z) = {{f(z)^2+A(z)}\over{f(z)-1}} \] where he defines \[ \Delta\varphi(z)=\varphi(z+1)-\varphi(z) \] with the standard iteration of the difference operator; \(A(z)\) is a meromorphic function. He considers: meromorphic solutions of the difference Riccati equation and the discrete analogue of the cross ratio; linear second order difference equations in the complex domain and growth problems for the solutions.