an:05702381 Zbl 1190.26030 Tomovski, \v Zivorad; Pog\'any, Tibor K. New upper bounds for Mathieu-type series. EN Banach J. Math. Anal. 3, No. 2, 9-15, electronic only (2009). ISSN 1735-8787/e 2009

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*26D15 33E20 33E10 Mathieu series; upper bounds; Hardy-Hilbert integral inequality Mathieu's series is defined by $$ S(r)=\sum_{n=1}^{\infty}\frac{2n}{(n^2+r^2)^2}. $$ The corresponding alternating series is $$ \tilde{S}(r)=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{2n}{(n^2+r^2)^2}. $$ The authors obtain upper bounds for the functions $S(r)$ and $\tilde{S}(r)$. Stamatis Koumandos (Nicosia)