A matrix approach to some second-order difference equations with sign-alternating coefficients

Abstract

In this paper, we analyse and unify some recent results on the double sequence {yn,k}, for n, k ? 1, defined by the second-order difference equation (Formula presented.) with (Formula presented.) and (Formula presented.), in terms of matrix theory and orthogonal polynomials theory. Moreover, we provide a general solution to (Formula presented.) using a closely related approach. We discuss briefly other recent problems involving a general recurrence relation of second order and relate them with the existing literature.