Functional inequalities involving special functions
type: Item
instance of: scholarly article
title: Functional inequalities involving special functions
zbMATH Open document ID: 1091.33002
author: Árpád Baricz
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-05-29T00:00:00Z
review text: Let \(_2F_1 (a,b;c;x)\) be a hypergeometric function and let \[ m(r) = {}_2F_1 (a,b;a+b;(1-r^2))/_2F_1 (a,b;a+b;r^2), \quad r \in (0,1). \] The author shows that \[ m(r) + m(s) \geq 2m[ \sqrt(1- \sqrt(( 1-r^2)(1-s^2)))]. \] If \(u_p\) is the generalized and normalized Bessel function and \(\sigma(r) = u_p(1 - r^2)/ u_p (r^2)\), the author proves that \[ \sqrt (\sigma(r_1)\sigma(r_2)) \leq \sigma( \sqrt(r_1 r_2)), \quad c < 0, \quad 2p+b+1 > 0. \]
reviewed by: P. R. Parthasarathy
Mathematics Subject Classification ID: 33C15
Mathematics Subject Classification ID: 26D20
zbMATH DE Number: 5028722
zbMATH Keywords: Bessel functions
zbMATH Keywords: hypergeometric functions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.06.052
OpenAlex ID: W4213246751
cites work: Functional Inequalities for Complete Elliptic Integrals and Their Ratios
cites work: Hypergeometric functions and elliptic integrals
cites work: Functional inequalities for the quotients of hypergeometric functions
cites work: Q3539441
cites work: Analytic Inequalities
cites work: Asymptotic expansions and inequalities for hypergeometric function
cites work: Duplication inequalities for the ratios of hypergeometric functions
cites work: Q5562752
DOI: 10.1016/J.JMAA.2005.06.052
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