International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2547-2554
Notes on double inequalities of Mathieu's series
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.