an: Zbl 1190.26030
au: Tomovski, \v Zivorad; Pog\'any, Tibor K.
ti: New upper bounds for Mathieu-type series.
la: EN
so: Banach J. Math. Anal. 3, No. 2, 9-15, electronic only (2009).
py: 2009
dt: J
cc: *26D15 33E20 33E10
ut: Mathieu series; upper bounds; Hardy-Hilbert integral inequality
ab: 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 $\tilde{S}(r)$.
rv: Stamatis Koumandos (Nicosia)