2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227018It is well known that the family of Hahn polynomials $\{h_n^{α,β}(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $Δ$-Sobolev orthogonality. We also present an analogous result for dual-Hahn, Krawtchouk, and Racah polynomials and give the limit relations between them for all $n\in \XX N_0$. Furthermore, in order to get this results for the Krawtchouk polynomials we will get a more general property of orthogonality for Meixner polynomials.2 figures, 20 pagesClassical Analysis and ODEs33C45, 26C05text