2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168675The objective of this paper is twofold: (i) to survey existing results of generalized polynomials on time scales, covering definitions and properties for both delta and nabla derivatives; (ii) to extend previous results by using the more general notion of diamond-alpha derivative on time scales. We introduce a new notion of combined-polynomial series on a time scale, as a convex linear combination of delta and nabla generalized series. Main results are formulated for homogenous time scales. As an example, we compute diamond-alpha derivatives on time scales for delta and nabla exponential functions.Accepted to the 8th Portuguese Conference on Automatic Control -- CONTROLO'2008, 21 to 23 July 2008, UTAD University, Vila Real, PortugalClassical Analysis and ODEs40C99; 39A13; 40A30text