A NEW MORE ACCURATE HILBERT-TYPE INEQUALITYINVOLVING ONE PARTIAL SUM

By using the weight coefficients, the Euler-Maclaurin summation formula and Abel summation by parts formula, a new more accurate Hilbert-type inequality with the power function as the internal variables involving one partial sum is given. The equivalent conditions of the best value related to a few parameters are obtained, and some particular inequalities are considered. We also provide the equivalent forms and the operator expressions.