A complete monotonicity property of the gamma function
type: Item
instance of: scholarly article
title: A complete monotonicity property of the gamma function
zbMATH Open document ID: 1046.33001
author: Feng Qi
author: Chao-Ping Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-19T00:00:00Z
review text: A real valued \(C^{\infty}\) function \(f\) is strictly completely monotonic on an interval \(I\) if \((-1)^k f^{(k)}(x)>0\) for all \(x\in I,\, k\in \mathbb{N}\). For the gamma function the result is offered that \(x\mapsto 1-\ln x+(\ln \Gamma(x+1))/x\) is strictly completely monotonic on \(]0,\infty[\) and its limits at \(0\) and \(\infty\) are \(\infty\) and \(0,\) respectively.
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 26A24
zbMATH DE Number: 2092949
zbMATH Keywords: gamma function
zbMATH Keywords: complete monotonicity
reviewed by: János Aczél
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.026
OpenAlex ID: W2077314575
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DOI: 10.1016/J.JMAA.2004.04.026
description: scientific article; zbMATH DE number 2092949