关联多个特殊函数的Hilbert型不等式及应用  

A Hilbert-type Inequality Related to Several Special Functions and Applications

作　　者：有名辉[1] 宋维[1] 王晓宇 YOU Ming-hui;SONG Wei;WANG Xiao-yu(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China)

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：《佳木斯大学学报（自然科学版）》2020年第6期159-162,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：浙江省教育厅一般科研资助项目(Y201737260);浙江机电职业技术学院科教融合一般项目(A-0271-20-007)。

摘　　要：通过引入参数,构建一个第一象限内与指数函数和对数函数关联的混合核函数,并建立与之对应的Hilbert型积分不等式,推广了一些已有结果.所得不等式的常数因子被证明是最佳的,且与多个特殊函数及特殊常数有关,如Digamma函数、Gamma函数、Riemann Zeta函数以及Euler常数.另外,赋予参数特殊的数值,文末还给出了若干特殊结果.By introducing some parameters,we construct a mixed kernel function associated with exponent function and logarithmic function in the first quadrant,and the corresponding Hilbert-type integral inequality is established.The obtained result is proved to be the generalization of some existing results.In addition,the constant factor of the inequality is proved to be optimal,and it is combined with several special functions,such as Digamma function,Gamma function,Riemann Zeta function.In addition,we also prove that the optimal constant factor is related to Euler constant.At last,by specifying the value of parameters,some special results are given at the end of the paper.

关 键 词：HILBERT型不等式 Digamma函数 Riemann Zeta函数 GAMMA函数 EULER常数 

分 类 号：O174.1[理学—数学]