Journal of Applied Mathematics

New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities

Hua-feng Ge

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 137507, 7 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331817615

Digital Object Identifier
doi:10.1155/2012/137507

Mathematical Reviews number (MathSciNet)
MR2830976

Zentralblatt MATH identifier
1294.11016

Citation

Ge, Hua-feng. New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities. J. Appl. Math. 2012 (2012), Article ID 137507, 7 pages. doi:10.1155/2012/137507. https://projecteuclid.org/euclid.jam/1331817615


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