Error bounds for asymptotic solutions of second-order linear difference equations
The authors establish in detail the error bounds for asymptotic solutions of the second order linear difference equation \[ y(n+2)+a(n) y(n+1)+b(n) y(n)=0 \] where \(a(n)\), \(b(n)\) have asymptotic expansions \[ a(n) \sim \sum^\infty_{s=0} {a_s \over n^s}, \quad b(n) \sim \sum^\infty_{s=0} {b_s \over n^s}, \quad n \to \infty. \] For related results see the paper of \textit{R. Wong} and \textit{H. Li} [J. Comput. Appl. Math. 41, No. 1-2, 65-94 (1992; Zbl 0758.39005)].
scientific article; zbMATH DE number 910311