Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0699.10013
Sándor, J.; Tóth, L.
A remark on the gamma function. (English)
[J] Elem. Math. 44, No.3, 73-76 (1989). ISSN 0013-6018; ISSN 1420-8962/e

Let P denote the arithmetic function defined by $P(n)=\prod\sb{k=1,...,n;(k,n)=1}\Gamma (k/n)$, where $\Gamma$ is the Euler gamma function. The authors give an explicit formula for P(n) and establish an asymptotic formula with remainder term for the summatory function of log P(n). The motivation for the study of the function P arises from the relation log P(n)$\sim \phi (n) \log \sqrt{2\pi}$ (n$\to \infty)$, where $\phi$ is the Euler totient function.
[P.Hankkanen]

MSC 2000:: *11A25 Arithmetic functions, etc.

Keywords: von Mangoldt function; Euler gamma function; asymptotic formula; Euler totient function

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