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