Rebocho, Maria das Neves2023-01-122023-01-122022-05Rebocho, M.N. (2022). On the second-order holonomic equation for Sobolev-type orthogonal polynomials. Applicable Analysis 101, no. 1, 314 - 336.http://hdl.handle.net/10400.6/12640It is presented a general approach to the study of orthogonal polynomials related to Sobolev inner products which are defined in terms of divided-difference operators having the fundamental property of leaving a polynomial of degree $n-1$ when applied to a polynomial of degree $n$. This paper gives analytic properties for the orthogonal polynomials, including the second order holonomic difference equation satisfied by them.engSobolev-type orthogonal polynomialsSpecial non-uniform latticesSemiclassical classHolonomic difference equationjournal articlehttps://doi.org/10.1080/00036811.2020.1742881