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

Journal of inequalities and applications

article

Xing Shou Huang¹  Ricai Luo¹  Bicheng Yang² 

[1] School of Mathematics and Statistics, Hechi University;Department of Mathematics, Guangdong University of Education

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

DOI  :  10.1186/s13660-020-2293-2

学科分类：电力

来源: SpringerOpen

【 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.

【 授权许可】

CC BY