Abstract and Applied Analysis 
Volume 2007 (2007), Article ID 94854, 10 pages
doi:10.1155/2007/94854
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

Recommended by Lance L. Littlejohn

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.