WKB (Liouville-Green) analysis of second order difference equations and applications (Q1196885)

A discrete analog is given of the WKB or Liouville-Green approximation for the solutions of second order difference equations of the type \(d(n+1)y(n+1)-q(n)y(n)+y(n-1)=0,\) where \(d(n)\) and \(q(n)\) are sequences of complex numbers with \(d(n) \neq0,\;n=0,1,2,\ldots\). The methods are used to obtain asymptotics for polynomials orthogonal on an infinite interval whose recurrence coefficients are regularly or slowly varying.