Diamond-alpha Polynomial Series on Time Scales

Details Diamond-alpha Polynomial Series on Time Scales Diamond-alpha Polynomial Series on Time Scales

2008-05-02

arxiv.org/abs/0805.0274v1

Int. J. Math. Stat. 5 (2009), No. A09, 92--101

Mathematics

Classical Analysis and ODEs

Accepted to the 8th Portuguese Conference on Automatic Control -- CONTROLO'2008, 21 to 23 July 2008, UTAD University, Vila Rea

Scientific paper

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.

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