Abstract and Applied Analysis
Volume 2007 (2007), Article ID 94854, 10 pages
Research Article

Some New Bounds for Mathieu's Series

Abdolhossein Hoorfar1 and Feng Qi2

1Department of Irrigation Engineering, College of Agriculture and Natural Resources, University of Tehran, Karaj 31587-77871, Iran
2Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China

Received 9 February 2007; Revised 3 June 2007; Accepted 6 August 2007

Academic Editor: Lance L. Littlejohn

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.


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.