A superadditive property of Hadamard's gamma function
type: Item
instance of: scholarly article
title: A superadditive property of Hadamard's gamma function
zbMATH Open document ID: 1180.33001
author: Horst Alzer
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2009-10-26T00:00:00Z
review text: Hadamard introduced his gamma function in 1894 by \[ H(x)= {1\over\Gamma(1- x)}\cdot{d\over dx}\log\Biggl({\Gamma(1/2- x/2)\over \Gamma(1- x/2)}\Biggr), \] where \(\Gamma\) is the Euler gamma function. The author studies monotonicity, convexity and superadditive properties of this function. For example \(H\) is strictly increasing in \([3,\infty)\); strictly convex in \([1.6,\infty)\), and superadditive in \([a,\infty)\), where \(a\) is the single solution to \(H(2t)= 2H(t)\) in \(t\in[1.5,\infty)\). A comprehensive bibliography on gamma functions and their inequalities can be fund at \url{http://www.math.ubbcluj.ro/~jsandor/letolt/art42}.
reviewed by: József Sándor
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 39B62
zbMATH DE Number: 5620549
zbMATH Keywords: Euler gamma function
zbMATH Keywords: psi function
zbMATH Keywords: Hadamard gamma function
zbMATH Keywords: superadditive inequalities
MaRDI profile type: Publication
full work available at URL: s12188-008-0009-5
OpenAlex ID: W2087320643
Wikidata QID: Q56486352
cites work: Q5558293
cites work: On some inequalities for the gamma and psi functions
cites work: A power mean inequality for the gamma function
cites work: Mean-value inequalities for the polygamma functions
cites work: A subadditive property of the gamma function.
cites work: Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz
cites work: Q4527133
DOI: 10.1007/S12188-008-0009-5
description: scientific article; zbMATH DE number 5620549