Ferreira González, CheloLópez García, José LuisPérez Sinusía, Ester2018-12-142019-11-0820181660-5446 (Print)1660-5454 (Electronic)10.1007/s00009-018-1267-9https://academica-e.unavarra.es/handle/2454/31783This is a post-peer-review, pre-copyedit version of an article published in Mediterranean Journal of Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s00009-018-1267-9We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find the asymptotic behavior for large |Λ|of the solutions of this equation: (i) an iterative method based on a fixed point method and (ii) a discrete version of Olver’s method for second-order linear differential equations. Both methods provide an asymptotic expansion of every solution of this equation. The expansion given by the first method is also convergent and may be applied to nonlinear problems. Bounds for the remainders are also given. We illustrate the accuracy of both methods for the modified Bessel functions and the associated Legendre functions of the first kind.16 p.application/pdfeng© Springer Nature Switzerland AG 2018Second-order difference equationsAsymptotic expansionsGreen’s functionsOlver’s methodinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia