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- W2021549280 abstract "We obtain new sharp bounds for the Bernoulli numbers:<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy=false>(</mml:mo><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>!</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo>)</mml:mo><mml:mo><</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mo>≤</mml:mo><mml:mrow><mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>)</mml:mo><mml:mrow><mml:mrow><mml:mi>ζ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mn>2</mml:mn><mml:mi>k</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>!</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>, </mml:mo><mml:mi>k</mml:mi><mml:mo>∈</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>, 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." @default.
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- W2021549280 date "2012-01-01" @default.
- W2021549280 modified "2023-10-17" @default.
- W2021549280 title "New Sharp Bounds for the Bernoulli Numbers and Refinement of Becker-Stark Inequalities" @default.
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- W2021549280 doi "https://doi.org/10.1155/2012/137507" @default.
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