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arXiv · 0805.0274

Diamond-alpha Polynomial Series on Time Scales

Dorota Mozyrska·Delfim F. M. Torres
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Abstract

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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BibTeXRIS

Dorota Mozyrska, Delfim F. M. Torres. 2008-05-02. Diamond-alpha Polynomial Series on Time Scales. https://arxiv.org/abs/0805.0274

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