Some New Bounds for Mathieu's Series

Hoorfar, Abdolhossein; Qi, Feng

doi:https://doi.org/10.1155/2007/94854

Abstract and Applied Analysis

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Volume 2007 | Article ID 094854 | https://doi.org/10.1155/2007/94854

Some New Bounds for Mathieu's Series

Abdolhossein Hoorfar¹and Feng Qi²

Academic Editor: Lance L. Littlejohn

Received09 Feb 2007

Revised03 Jun 2007

Accepted06 Aug 2007

Published03 Oct 2007

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 ζ(3) are deduced.

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Copyright

Copyright © 2007 Abdolhossein Hoorfar and Feng Qi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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