Marcellán, FranciscoMendes, AnaPijeira, Héctor2026-03-062026-03-062013-10Marcellán, F., Mendes, A., & Pijeira, H. (2013). Bases of the space of solutions of some fourth-order linear difference equations: applications in rational approximation. Journal of Difference Equations and Applications, 19(10), 1632–1644. https://doi.org/10.1080/10236198.2013.7695311023-61981563-5120http://hdl.handle.net/10400.8/15794It is very well known that a sequence of polynomials {Qn(x)}∞n=0 orthogonal with respect to a Sobolev discrete inner product 〈f,g〉s = ∫Ifg dμ+λf′(0)g′(0), λ ∈ ℝ+ where μ is a finite Borel measure and I is an interval of the real line, satisfies a five-term recurrence relation. In this contribution we study other three families of polynomials which are linearly independent solutions of such a five-term linear difference equation and, as a consequence, we obtain a polynomial basis of such a linear space. They constitute the analogue of the associated polynomials in the standard case. Their of {Qn(x)}∞n=0 explicit expression in terms of using an integral representation is given. Finally, an application of these polynomials in rational approximation is shown.engOrthogonal polynomialsRecurrence relationDifference equationsjournal article10.1080/10236198.2013.769531