Copyright © 2009 Zhou Yu 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.

Abstract

It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters m   (m∈N) and λ   (λ>0). The constant factors expressed by the Euler number and π as well as by the Bernoulli number and π, respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.