On an improvement of the Hardy-Hilbert type inequality

TL;DR

This paper improves a Hardy-Hilbert type inequality by effectively estimating weight coefficients using Euler-Maclaurin expansion, leading to sharper bounds and specific applications.

Contribution

It introduces a novel method for estimating weight coefficients, enhancing the Hardy-Hilbert inequality with new bounds and applications.

Findings

Established an improved Hardy-Hilbert type inequality

Utilized Euler-Maclaurin expansion for the zeta function

Provided specific applications of the improved inequality

Abstract

In this paper, by estimating the weight coefficient effectively, we establish an improvement of a Hardy-Hilbert type inequality proved by B.C. Yang, our main tool is Euler-Maclaurin expansion for the zeta function. As applications, some particular results are considered