New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities
We obtain new sharp bounds for the Bernoulli numbers: 2(2n)!/(π2n(22n−1))<|B2n|≤(2(22k−1)/22k)ζ(2k)(2n)!/(π2n(22n−1)), n=k,k+1,…, k∈N+, and establish sharpening of Papenfuss's inequalities, the refinements of Becker-Stark, and Steckin's inequalities. Finally, we show a new simple proof...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/137507 |
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| _version_ | 1832553623317381120 |
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| author | Hua-feng Ge |
| author_facet | Hua-feng Ge |
| author_sort | Hua-feng Ge |
| collection | DOAJ |
| description | We obtain new sharp bounds for the Bernoulli numbers: 2(2n)!/(π2n(22n−1))<|B2n|≤(2(22k−1)/22k)ζ(2k)(2n)!/(π2n(22n−1)), n=k,k+1,…, k∈N+, and establish sharpening of Papenfuss's inequalities, the refinements of Becker-Stark, and
Steckin's inequalities. Finally, we show a new simple proof of Ruehr-Shafer inequality. |
| format | Article |
| id | doaj-art-a0dac2eb05f94ed9983c5fa0306e8ee1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a0dac2eb05f94ed9983c5fa0306e8ee12025-02-03T05:53:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/137507137507New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark InequalitiesHua-feng Ge0Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, ChinaWe obtain new sharp bounds for the Bernoulli numbers: 2(2n)!/(π2n(22n−1))<|B2n|≤(2(22k−1)/22k)ζ(2k)(2n)!/(π2n(22n−1)), n=k,k+1,…, k∈N+, and establish sharpening of Papenfuss's inequalities, the refinements of Becker-Stark, and Steckin's inequalities. Finally, we show a new simple proof of Ruehr-Shafer inequality.http://dx.doi.org/10.1155/2012/137507 |
| spellingShingle | Hua-feng Ge New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities Journal of Applied Mathematics |
| title | New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities |
| title_full | New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities |
| title_fullStr | New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities |
| title_full_unstemmed | New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities |
| title_short | New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities |
| title_sort | new sharp bounds for the bernoulli numbers and refinement of becker stark inequalities |
| url | http://dx.doi.org/10.1155/2012/137507 |
| work_keys_str_mv | AT huafengge newsharpboundsforthebernoullinumbersandrefinementofbeckerstarkinequalities |