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2012 New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities
Hua-feng Ge
J. Appl. Math. 2012: 1-7 (2012). DOI: 10.1155/2012/137507

Abstract

We obtain new sharp bounds for the Bernoulli numbers: 2 ( 2 n ) ! / ( π 2 n ( 2 2 n 1 ) ) < | B 2 n | ( 2 ( 2 2 k 1 ) / 2 2 k ) ζ ( 2 k ) ( 2 n ) ! / ( π 2 n ( 2 2 n 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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Hua-feng Ge. "New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities." J. Appl. Math. 2012 1 - 7, 2012. https://doi.org/10.1155/2012/137507

Information

Published: 2012
First available in Project Euclid: 15 March 2012

zbMATH: 1294.11016
MathSciNet: MR2830976
Digital Object Identifier: 10.1155/2012/137507

Rights: Copyright © 2012 Hindawi

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