A note on Turán type and mean inequalities for the Kummer function
type: Item
instance of: scholarly article
title: A note on Turán type and mean inequalities for the Kummer function
zbMATH Open document ID: 1162.33001
author: Roger W. Barnard
author: Michael B. Gordy
author: Kendall C. Richards
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-11-06T00:00:00Z
review text: The main result is the following: Suppose \(a,b> 0\). Then for any \(n\in\mathbb{N}\) with \(a,b\geq n-1\) \[ \phi(a,a+ b,x^2)> \phi(a+n, a+ b,x)\phi(a- n,a+ n,x) \] for all nonzero \(x\in\mathbb{R}\). Moreover, these expressions coincide with value 1 when \(x= 0\) and asymptotically for any \(x\) when \(b\to\infty\) (\(\phi\) is the Kummer confluent hypergeometric function). Few more results are obtained by utilizing the above-mentioned result. A possible application to modeling credit risk is indicated.
reviewed by: Pushpa N. Rathie
Mathematics Subject Classification ID: 33C15
zbMATH DE Number: 5362150
zbMATH Keywords: Kummer confluent hypergeometric function
zbMATH Keywords: Turán-type inequality
zbMATH Keywords: mean
zbMATH Keywords: generalized hypergeometric function
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.08.024
OpenAlex ID: W2086184496
cites work: An introduction to hypergeometric functions for economists
cites work: Q4222737
cites work: Turán type inequalities for generalized complete elliptic integrals
cites work: Functional inequalities involving Bessel and modified Bessel functions of the first kind
cites work: Turán type inequalities for hypergeometric functions
cites work: Q3476890
cites work: Q4441514
cites work: Q4515165
cites work: Monotonicity properties of determinants of special functions
cites work: A Turán Inequality Arising in Information Theory
cites work: Q3999270
cites work: Q5800445
DOI: 10.1016/J.JMAA.2008.08.024
description: scientific article; zbMATH DE number 5362150