On a new extended half-discrete Hilbert’s inequality involving partial sums

Abstract

By applying the weight functions, the idea of introducing parameters, and Euler-Maclaurin summation formula, a new extended half-discrete Hilbert's inequality with the homogeneous kernel and the beta, gamma function is given. The equivalent statements of the best possible constant factor related to a few parameters are considered. As applications, a corollary about the case of the non-homogeneous kernel and some particular cases are obtained. MSC: 26D15