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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Hindawi Limited
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/137507 |