International Journal of Mathematics and Mathematical Sciences 
Volume 2005 (2005), Issue 16, Pages 2547-2554
doi:10.1155/IJMMS.2005.2547

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

Abstract

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.