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
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.