On a new extended half-discrete Hilbert’s inequality involving partial sums
Abstract 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 re...
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SpringerOpen
2020-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-020-2293-2 |
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doaj-43136ec9be064ac78ca4e1d0ec34325b2021-01-31T12:08:32ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-01-012020111410.1186/s13660-020-2293-2On a new extended half-discrete Hilbert’s inequality involving partial sumsXing Shou Huang0Ricai Luo1Bicheng Yang2School of Mathematics and Statistics, Hechi UniversitySchool of Mathematics and Statistics, Hechi UniversityDepartment of Mathematics, Guangdong University of EducationAbstract 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.https://doi.org/10.1186/s13660-020-2293-2Weight functionHalf-discrete Hilbert’s inequalityParameterEuler–Maclaurin summation formulaGamma functionBeta function |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xing Shou Huang Ricai Luo Bicheng Yang |
| spellingShingle |
Xing Shou Huang Ricai Luo Bicheng Yang On a new extended half-discrete Hilbert’s inequality involving partial sums Journal of Inequalities and Applications Weight function Half-discrete Hilbert’s inequality Parameter Euler–Maclaurin summation formula Gamma function Beta function |
| author_facet |
Xing Shou Huang Ricai Luo Bicheng Yang |
| author_sort |
Xing Shou Huang |
| title |
On a new extended half-discrete Hilbert’s inequality involving partial sums |
| title_short |
On a new extended half-discrete Hilbert’s inequality involving partial sums |
| title_full |
On a new extended half-discrete Hilbert’s inequality involving partial sums |
| title_fullStr |
On a new extended half-discrete Hilbert’s inequality involving partial sums |
| title_full_unstemmed |
On a new extended half-discrete Hilbert’s inequality involving partial sums |
| title_sort |
on a new extended half-discrete hilbert’s inequality involving partial sums |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1029-242X |
| publishDate |
2020-01-01 |
| description |
Abstract 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. |
| topic |
Weight function Half-discrete Hilbert’s inequality Parameter Euler–Maclaurin summation formula Gamma function Beta function |
| url |
https://doi.org/10.1186/s13660-020-2293-2 |
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