An inequality for the product of two integrals relating to the incomplete gamma function
type: Item
instance of: scholarly article
title: An inequality for the product of two integrals relating to the incomplete gamma function
zbMATH Open document ID: 0947.33002
DOI: 10.1155/S1025583400000035
author: Á. Elbert
author: A. Laforgia
published in: Journal of Inequalities and Applications
publication date: 2000-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/120572
review text: Authors offer as main result the inequality \(F(x,p):=\int_0^x \exp(t^p) dt \int_x^{\infty} \exp(-t^p) dt <1/4\) for \(x\) nonnegative and \(p\) greater than the unique solution of \(\sup_{x>0} F(x,p)=1/4\) \((p\geq 1).\) Moreover inequalities (bounds) for the two integrals in \(F(x,p)\) are offered.
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 26D07
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1437135
zbMATH Keywords: incomplete gamma functions
zbMATH Keywords: inequalities
zbMATH Keywords: bounds
zbMATH Keywords: complete gamma functions
reviewed by: János Aczél
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1437135