On further strengthened Hardy-Hilbert's inequality
We obtain an inequality for the weight coefficient ω(q,n) (q>1, 1/q+1/q=1, n∈ℕ) in the form ω(q,n)=:∑m=1∞(1/(m+n))(n/m)1/q<π/sin(π/p)−1/(2n1/p+(2/a)n−1/q) where 0<a<147/45, as n≥3; 0<a<(1−C)/(2C−1), as n=1,2, and C is an Euler constant. We show a generalization and improvement of...
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Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204205270 |
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doaj-0da8deb1db7846bf859897379e0a52e72020-11-25T00:23:43ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004271423142710.1155/S0161171204205270On further strengthened Hardy-Hilbert's inequalityLü Zhongxue0School of Science, Nanjing University of Science & Technology, Nanjing 210094, ChinaWe obtain an inequality for the weight coefficient ω(q,n) (q>1, 1/q+1/q=1, n∈ℕ) in the form ω(q,n)=:∑m=1∞(1/(m+n))(n/m)1/q<π/sin(π/p)−1/(2n1/p+(2/a)n−1/q) where 0<a<147/45, as n≥3; 0<a<(1−C)/(2C−1), as n=1,2, and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.http://dx.doi.org/10.1155/S0161171204205270 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lü Zhongxue |
| spellingShingle |
Lü Zhongxue On further strengthened Hardy-Hilbert's inequality International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Lü Zhongxue |
| author_sort |
Lü Zhongxue |
| title |
On further strengthened Hardy-Hilbert's inequality |
| title_short |
On further strengthened Hardy-Hilbert's inequality |
| title_full |
On further strengthened Hardy-Hilbert's inequality |
| title_fullStr |
On further strengthened Hardy-Hilbert's inequality |
| title_full_unstemmed |
On further strengthened Hardy-Hilbert's inequality |
| title_sort |
on further strengthened hardy-hilbert's inequality |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
We obtain an inequality for the weight coefficient ω(q,n)
(q>1, 1/q+1/q=1, n∈ℕ) in the
form ω(q,n)=:∑m=1∞(1/(m+n))(n/m)1/q<π/sin(π/p)−1/(2n1/p+(2/a)n−1/q) where 0<a<147/45,
as n≥3; 0<a<(1−C)/(2C−1), as n=1,2, and C is an Euler
constant. We show a generalization and improvement of Hilbert's
inequalities. The results of the paper by Yang and Debnath are
improved. |
| url |
http://dx.doi.org/10.1155/S0161171204205270 |
| work_keys_str_mv |
AT luzhongxue onfurtherstrengthenedhardyhilbertsinequality |
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1725355357223518208 |