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New Upper Bounds for Mathieu-Type Series

Tomovski, Živorad and Pogány, Tibor K (2008) New Upper Bounds for Mathieu-Type Series. Research report collection, 11 (4).

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Abstract

The Mathieu’s series S(r) was considered firstly by É.L. Mathieu in 1890; its alternating variant Š(r) has been recently introduced by Pogány et al. [Some families of Mathieu a-series and alternating Mathieu a-series, 2006] where various bounds have been established for S, Š. In this note we obtain new upper bounds over S(r), Š(r) with the help of Hardy–Hilbert double integral inequality.

Item Type: Article
Uncontrolled Keywords: Mathieu series, alternating Mathieu-series, Hardy-Hilbert integral inequality, upper bound inequality
Subjects: FOR Classification > 0101 Pure Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 10 Feb 2012 00:32
Last Modified: 23 May 2013 16:51
URI: http://vuir.vu.edu.au/id/eprint/17641
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