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2009 New upper bounds for Mathieu-type series
Tibor K. Pogany, Zivorad Tomovski
Banach J. Math. Anal. 3(2): 9-15 (2009). DOI: 10.15352/bjma/1261086704

Abstract

The Mathieu's series $S(r)$ was considered firstly by E.L. Mathieu in 1890, its alternating variant $\widetilde{S}(r)$ has been recently introduced by Pogany et al. [Appl. Math. Comput. 173 (2006), 69--108], where various bounds have been established for $S, \widetilde{S}$. In this note we obtain new upper bounds over $S(r), \widetilde{S}(r)$ with the help of Hardy--Hilbert double integral inequality.

Citation

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Tibor K. Pogany. Zivorad Tomovski. "New upper bounds for Mathieu-type series." Banach J. Math. Anal. 3 (2) 9 - 15, 2009. https://doi.org/10.15352/bjma/1261086704

Information

Published: 2009
First available in Project Euclid: 17 December 2009

zbMATH: 1190.26030
MathSciNet: MR2492004
Digital Object Identifier: 10.15352/bjma/1261086704

Subjects:
Primary: 26D15
Secondary: 33E20

Keywords: alternating Mathieu--series , Hardy--Hilbert integral inequality , Mathieu series , upper bound inequality

Rights: Copyright © 2009 Tusi Mathematical Research Group

Vol.3 • No. 2 • 2009
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