Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions
type: Item
instance of: scholarly article
title: Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions
zbMATH Open document ID: 1116.26019
DOI: 10.1155/JIA/2006/48727
author: A. Laforgia
author: P. Natalini
published in: Journal of Inequalities and Applications
publication date: 2006-05-29T00:00:00Z
full work available at URL: https://eudml.org/doc/127695
review text: Let \(\Gamma(a)\) and \(\Gamma(a;z)\) denote the gamma and the incomplete gamma functions, respectively. Some monotonicity results for the gamma function are proved and a lower bound for the function \[ \int_0^xe^{-t^p}dt=[\Gamma(1/p)-\Gamma(1/p;x^p)]/p \] with \(p>1\) for \(0<x<[9(3p+1)/4(2p+1)]^{1/p}\) is extended to \(x>0\).
reviewed by: Feng Qi
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 5028499
zbMATH Keywords: lower bound
zbMATH Keywords: extension
Wikidata QID: Q59212581
MaRDI profile type: Publication
cites work: On some inequalities for the incomplete gamma function
cites work: An inequality for the product of two integrals relating to the incomplete gamma function
cites work: Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
cites work: Q4297533
cites work: Inequalities for the Incomplete Gamma and Related Functions
OpenAlex ID: W2022897586
description: scientific article