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

[摘要] 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.

[学科分类] 电力

[关键词] Weight function;Half-discrete Hilbert’s inequality;Parameter;Euler–Maclaurin summation formula;Gamma function;Beta function