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
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
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