Asymptotic representation of solutions of linear second order difference equations (Q1191650)

The authors obtain asymptotic formulae for the solutions of the difference equation \[ \Delta(p(R)y(k+1))+(f(k)+g(k))y(k)=0 \] whenever a fundamental system of solutions \(\{\varphi_ 1,\varphi_ 2\}\) of the unperturbed equation \(\Delta (p(R)z(k+1)+f(k)z(k)=0\) is known. Here \(\Delta\) is the operator defined by \(\Delta y(k)=y(k+1)-y(k)\).