2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71837We apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of $λ$-umbral calculi parameterized by $λ$ in the base ring.22 pagesRings and AlgebrasCombinatoricsNumber Theory16A06, 05A40, 13A99,11B65text