Precise estimates for differences of the Gaussian hypergeometric function
type: Item
instance of: scholarly article
title: Precise estimates for differences of the Gaussian hypergeometric function
zbMATH Open document ID: 0885.33002
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-04-22T00:00:00Z
review text: For given \(a,b,c,d\in (0,\infty)\), \(a\leq b\), and \(c< d\), the authors study the problem of comparing the Gaussian hypergeometric functions \(F(a,b; a+b; 1-x^c)\) and \(F(a-\delta, b+\delta; a+b; 1- x^d)\). In particular they solve some open problems by determining \(\sup\{\delta\in (0,\infty): F(a,b; a+b; 1-x^c)< F(a-\delta, b+\delta; a+b; 1-x^d)\), \(x\in (0,1)\}\).
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 1115449
zbMATH Keywords: gamma function
zbMATH Keywords: Gaussian hypergeometric functions
author: G. D. Anderson
author: Song-Liang Qiu
author: M. Vuorinen
reviewed by: Janusz Matkowski
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5641
OpenAlex ID: W2017221560
cites work: Q3661894
cites work: Q5535091
cites work: Inequalities for Zero-Balanced Hypergeometric Functions
cites work: Hypergeometric functions and elliptic integrals
cites work: Inequalities for quasiconformal mappings in space
cites work: Ramanujan and hypergeometric and basic hypergeometric series
cites work: Q3995284
cites work: Ramanujan's Theories of Elliptic Functions to Alternative Bases
cites work: Inequalities for compound mean iterations with logarithmic asymptotes
cites work: Asymptotic expansions and inequalities for hypergeometric function
cites work: Generating Functions for Bessel and Related Polynomials
cites work: Q3844537
DOI: 10.1006/JMAA.1997.5641
description: scientific article; zbMATH DE number 1115449