Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0960.11016
Alzer, Horst
Sharp bounds for the Bernoulli numbers. (English)
[J] Arch. Math. 74, No.3, 207-211 (2000). ISSN 0003-889X; ISSN 1420-8938/e

The classical Bernoulli numbers $B_n$ $(n=0,1,2\ldots)$ can be defined by $$ \frac{x}{e^x-1}=\sum_{n=0}^\infty B_n\frac{x^n}{n!}, $$ $|x|< 2\pi$. In the paper under review the author gives the best possible constants $\alpha$ and $\beta$ such that $$ \frac{2(2n)!}{(2\pi)^{2n}}\frac 1{1-2^{\alpha-2n}} \le |B_{2n}|\le \frac{2(2n)!}{(2\pi)^{2n}}\frac 1{1-2^{\beta-2n}} $$ holds for all integers $n\ge 1$, namely $\alpha=0$ and $\beta=2+\frac{\log(1-6/\pi^2)}{\log(2)}\approx 0.6491\ldots$.
[Helmut Müller (Hamburg)]

MSC 2000:: *11B68 Bernoulli numbers, etc.

Keywords: Bernoulli numbers

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]