Some New Bounds for Mathieu's Series

Abdolhossein Hoorfar; Feng Qi

doi:10.1155/2007/94854

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Home > Journals > Abstr. Appl. Anal. > Volume 2007 > Article

2007 Some New Bounds for Mathieu's Series

Abdolhossein Hoorfar, Feng Qi

Abstr. Appl. Anal. 2007: 1-10 (2007). DOI: 10.1155/2007/94854

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Abstract

Two upper and lower bounds for Mathieu's series are established, which refine to a certain extent a sharp double inequality obtained by Alzer-Brenner-Ruehr in 1998. Moreover, the very closer lower and upper bounds for $\zeta (3)$ are deduced.