New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities
نویسنده
چکیده
Copyright q 2012 Hua-feng Ge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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.
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عنوان ژورنال:
- J. Applied Mathematics
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012