  The 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.
