New upper bounds for Mathieu-type series
Tomovski, Zivorad ; Pogany, Tibor K.
Banach J. Math. Anal., Tome 3 (2009) no. 2, p. 9-15 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Mathieu series,  alternating Mathieu--series,  upper bound inequality,  Hardy--Hilbert integral inequality,  26D15,  33E20 
@article{1261086704,
     author = {Tomovski, Zivorad and Pogany, Tibor K.},
     title = {New upper bounds for Mathieu-type series},
     journal = {Banach J. Math. Anal.},
     volume = {3},
     number = {2},
     year = {2009},
     pages = { 9-15},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1261086704}
}

Tomovski, Zivorad; Pogany, Tibor K. New upper bounds for Mathieu-type series. Banach J. Math. Anal., Tome 3 (2009) no. 2, pp.  9-15. http://gdmltest.u-ga.fr/item/1261086704/