几个基本Hilbert型不等式的统一推广  

On a Unified Extension of Several Basic Hilbert-type Inequalities

作　　者：有名辉[1] YOU Minghui(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou,Zhejiang 310053)

机构地区：[1]浙江机电职业技术学院数学教研室,浙江杭州310053

出　　处：《绍兴文理学院学报》2020年第4期62-67,106,共7页Journal of Shaoxing University

摘　　要：通过引进多个参数,构建一个第一象限内的非齐次核函数,并由此建立了具有最佳常数因子的Hilbert型不等式.通过简单的变量替换,把非齐次型的Hilbert型不等式演化为齐次型.通过对参数赋值,并借助余切函数的有理分式展开,得到最佳常数因子与余切函数高阶导数关联的Hilbert型不等式,推广了若干基本的Hilbert型不等式和一些经典结果.By introducing several parameters,a non-homogeneous kernel function in the first quadrant was constructed,and the corresponding Hilbert-type inequality with the optimal constant factor established.By means of simple variable substitution,the non-homogeneous Hilbert-type inequality was transformed into a homogeneous type.By specifying parameters and using the rational fraction expansion of the cotangent function,the Hilbert-type inequalities with the optimal constant factor related to the higher derivative of the cotangent function were obtained,which generalizes some basic Hilbert type inequalities and some classical results.

关 键 词：HILBERT型不等式 Catalan常数 余切函数 有理分式展开 

分 类 号：O174.1[理学—数学]