A simple elementary expression of Riemann function <i>ζ(s)</i>
We find a simple elementary expression of <i>ζ(s)</i>=∑ 1/<i>n<sup>s</sup></i> (<i>s</i>≥2) by Jordan inequality and Kober inequality,and evaluate the exact value of <i>ζ(s)</i>=∑ 1/<i>n<sup>s</sup></i> when <i&g...
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| Format: | Article |
| Language: | English |
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Academic Journals Center of Shanghai Normal University
2013-06-01
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| Series: | Journal of Shanghai Normal University (Natural Sciences) |
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| Online Access: | http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201303004&year_id=2013&quarter_id=3&falg=1 |
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doaj-781ee868e9c141c8a3f80a37960335d12020-11-25T02:30:42ZengAcademic Journals Center of Shanghai Normal UniversityJournal of Shanghai Normal University (Natural Sciences)1000-51371000-51372013-06-01423244247201303004A simple elementary expression of Riemann function <i>ζ(s)</i>XU Zhenhua0Nantong Guanhe Secondary SchoolWe find a simple elementary expression of <i>ζ(s)</i>=∑ 1/<i>n<sup>s</sup></i> (<i>s</i>≥2) by Jordan inequality and Kober inequality,and evaluate the exact value of <i>ζ(s)</i>=∑ 1/<i>n<sup>s</sup></i> when <i>s</i> is a positive even number.http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201303004&year_id=2013&quarter_id=3&falg=1Riemann functionfinite sum of trigonometric functionssum of series |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
XU Zhenhua |
| spellingShingle |
XU Zhenhua A simple elementary expression of Riemann function <i>ζ(s)</i> Journal of Shanghai Normal University (Natural Sciences) Riemann function finite sum of trigonometric functions sum of series |
| author_facet |
XU Zhenhua |
| author_sort |
XU Zhenhua |
| title |
A simple elementary expression of Riemann function <i>ζ(s)</i> |
| title_short |
A simple elementary expression of Riemann function <i>ζ(s)</i> |
| title_full |
A simple elementary expression of Riemann function <i>ζ(s)</i> |
| title_fullStr |
A simple elementary expression of Riemann function <i>ζ(s)</i> |
| title_full_unstemmed |
A simple elementary expression of Riemann function <i>ζ(s)</i> |
| title_sort |
simple elementary expression of riemann function <i>ζ(s)</i> |
| publisher |
Academic Journals Center of Shanghai Normal University |
| series |
Journal of Shanghai Normal University (Natural Sciences) |
| issn |
1000-5137 1000-5137 |
| publishDate |
2013-06-01 |
| description |
We find a simple elementary expression of <i>ζ(s)</i>=∑ 1/<i>n<sup>s</sup></i> (<i>s</i>≥2) by Jordan inequality and Kober inequality,and evaluate the exact value of <i>ζ(s)</i>=∑ 1/<i>n<sup>s</sup></i> when <i>s</i> is a positive even number. |
| topic |
Riemann function finite sum of trigonometric functions sum of series |
| url |
http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201303004&year_id=2013&quarter_id=3&falg=1 |
| work_keys_str_mv |
AT xuzhenhua asimpleelementaryexpressionofriemannfunctionizsi AT xuzhenhua simpleelementaryexpressionofriemannfunctionizsi |
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1724828394003103744 |