Asymptotic expansions for second-order linear difference equations (Q1195409)

Using the method of successive approximations, asymptotic formal series solutions of the linear second-order difference equation \(x_{n+2}+a_ nx_{n+1}+b_ nx_ n=0\), where \(a_ n\) and \(b_ n\) have asymptotic expansions of the form \(a_ n\sim\Sigma((c_ i/n^ i)\); \(i=0,\dots,\infty)\) and \(b_ n\sim\Sigma((d_ i/n^ i;i=0,\dots,\infty)\), for large values of \(n\), and \(d_ 0\neq 0\), are obtained.