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).


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
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Mathieu series, alternating Mathieu-series, Hardy-Hilbert integral inequality, upper bound inequality
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