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

Abstract

We obtain new sharp bounds for the Bernoulli numbers: , $n=k,k+1,\dots ,\hspace{0.17em}k\in N^{+}$, 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.