International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2547-2554

Notes on double inequalities of Mathieu's series

Feng Qi, Chao-Ping Chen, and Bai-Ni Guo

Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Henan Province, Jiaozuo City 454010, China

Received 7 January 2005; Revised 5 July 2005

Copyright © 2005 Feng Qi et al. 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.


Using the integral expression of Mathieu's series and some integral and analytic inequalities involving periodic functions and the generating function of Bernoulli numbers, we present several new inequalities and estimates for Mathieu's series and generalize Mathieu's series. Two open problems are proposed.