A remark on the gamma function
type: Item
instance of: scholarly article
title: A remark on the gamma function
zbMATH Open document ID: 0699.10013
author: László Tóth
author: József Sándor
published in: Elemente der Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141455
review text: Let P denote the arithmetic function defined by \(P(n)=\prod_{k=1,...,n;(k,n)=1}\Gamma (k/n)\), 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.
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 4145985
zbMATH Keywords: von Mangoldt function
zbMATH Keywords: Euler gamma function
zbMATH Keywords: asymptotic formula
zbMATH Keywords: Euler totient function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4145985